Map from Google - Austria

In Austria, a country largely covered by mountains and hills, we can distinguish between three types of climate: the continental climate of the narrow plain region of Vienna, similar to that of East-central Europe, with cold winters and warm summers, sometimes sultry; the climate of the other major cities (Salzburg, Graz, Linz, Innsbruck), located at higher altitude, with cold winters and fairly warm summers, which in summer receive a good amount of thunderstorms; and finally the Alpine climate of mountainous regions, freezing and snowy in winter, cool and with many afternoon thunderstorms in summer. In comparison with its Alpine "twin", Switzerland, Austria has a colder climate in winter, both because of the greater distance from the Atlantic Ocean, and of the proximity to the Russian plains.
Here are the average temperatures of Vienna.
Average temperatures - Vienna
ViennaJanFebMarAprMayJunJulAugSepOctNovDec
ViennaJFMAMJJASOND
Min (°C)-3-215101315151162-2
Max (°C)35101520232626211584
Min (°F)272834415055595952433628
Max (°F)374150596873797970594639

Precipitation is abundant in the mountains, where it exceeds 1,000 millimetres (40 inches) per year almost everywhere, and often 1.500 mm (60 in), while it's lower in the Vienna area, where only 535 mm (21 in) of rain or snow per year fall. However, precipitation is well distributed throughout the year, with a a slight increase in summer, because of heat thunderstorms.
Here is the average precipitation in Vienna, which is located in the least rainy area of the country.
Average precipitation - Vienna
ViennaJanFebMarAprMayJunJulAugSepOctNovDecYear
ViennaJFMAMJJASONDY
Prec. (mm)303035405560605050354535535
Prec.(in)1.21.21.41.62.22.42.4221.41.81.421.1
Days76778988657785

Vienna

Winter in Austria is cold everywhere, even in the Danube valley, but especially in the valleys located at higher altitude, and even more so in the mountains. In Vienna, the Austrian capital, the average temperature in January is around 0 °C (32 °F), but in cities located at higher altitude and in valleys among the mountains, the averages are even lower: in Klagenfurt, the capital of Carinthia, 450 metres (1,500 feet) above sea level, the average temperature in January is -4.5 °C (24 °F).
Fog and low clouds are common in the valleys, and in particular in the Danube Valley: in winter, fog occurs on average from 4 to 11 days per month.
Snow is quite common everywhere, except in the area of Vienna, where it is more rare.
The lowest temperatures have been recorded after outbreaks of cold air masses coming from Russia: in these cases the temperature can plunge to -15/-20 °C (-4/5 °F), or even lower, even in Vienna. The coldest records are -30 °C (-22 °F) in Innsbruck, Tyrol, 580 metres (1,900 feet) above sea level, and -31 °C (-24 °F) in Salzburg, at 435 m (1,400 ft).
Here are the average temperatures in Innsbruck.
Average temperatures - Innsbruck
InnsbruckJanFebMarAprMayJunJulAugSepOctNovDec
InnsbruckJFMAMJJASOND
Min (°C)-7-4-148111312940-4
Max (°C)14111621242624211482
Min (°F)192530394652555448393225
Max (°F)343952617075797570574636

In the mountainous regions, winter is obviously very cold and snowy, but it is sunnier than in the valleys, because the mountains are above the fog and low clouds layer that can form in periods of good weather, therefore they witness an acceptable amount of sunshine in this season.

Mountains in Austria

In January and February, between 1,200 and 1,800 metres (4,000 and 6,000 feet), the average minimum temperature ranges from -5 °C to -9 °C (16 to 23 °F), and the maximum temperature from -1 °C to +2 °C (30 and 36 °F). In high mountains, above 2,000 metres (6,500 feet), lows range from -8 °C to -14 °C (7 to 18 °F) and highs from -4 °C to -11 °C (12 to 25 °F).
Some areas of Austria are subject to down-slope winds coming from the mountains: when the Foehn blows from the south, the temperatures can suddenly increase, and snow can rapidly melt, causing floods and avalanches. In the south, in Carinthia, there's a variant of this wind called Jauk.

Summer is warm or even hot in the Vienna area, with some chance of thunderstorms in the afternoon, while it becomes very rainy in the rest of Austria, because of Atlantic fronts, which can cause unstable weather, triggering thunderstorms especially in the afternoon or evening.
Usually the rainiest month in Austria is July: for instance in Salzburg, where it rains almost every second day from May to August, more than 150 mm (6 in) of rain fall in this month, and the total amount of the three summer months (June, July and August) is 465 mm (18 in). On the contrary, the Vienna area is less rainy and a little sunnier.
Here is the average precipitation in Salzburg.
Average precipitation - Salzburg
SalzburgJanFebMarAprMayJunJulAugSepOctNovDecYear
SalzburgJFMAMJJASONDY
Prec. (mm)605580851151551601501007585751185
Prec.(in)2.42.23.13.34.56.16.35.93.933.3346.7
Days10101212121514131191112141

Usually, temperatures are often pleasantly warm during the day and cool at night: in Vienna the average daily temperature in July is around 20 °C (68 °F), and the maximum temperature is around 25/26 °C (77/79 °F) in Vienna and other major cities, but sometimes there may be hot and muggy days, especially in the plain (i.e. in the area of Vienna), with lows above 20 °C (68 °F) and highs above 30 °C (86 °F).
The highest recorded temperatures are 37.7 °C (100 °F) in Linz (East Tyrol), 37.8 °C (100 °F) in Salzburg, 38 °C (100.4 °F) in Feldkirch (Vorarlberg) and 40 °C (104 °F) in Bad Gleichenberg (Styria).

In the mountains, summer becomes cooler with increasing altitude, but it is equally prone to thunderstorms, to the point that the most abundant precipitation is recorded in this area. On average, at mid-mountain elevation, from 345 to 600 mm (13.5 to 23.5 in) of rain fall in the three summer months, while in high mountains, precipitation can reach as high as 800 mm (31.5 in), of which 265 mm (10.4 in) in the month of July.
Above 3,000 metres (10,000 ft), on Grossglockner, which is the highest mountain in Austria with its 3,798 metres (12,461 ft), the average temperature is around freezing even in July and August, as we can see from the average temperatures of the Sonnblick Observatory, located at 3,111 metres (10,207 ft) above sea level.
Average temperatures - Grossglockner
GrossglocknerJanFebMarAprMayJunJulAugSepOctNovDec
GrossglocknerJFMAMJJASOND
Min (°C)-14-14-13-10-5-300-3-6-10-13
Max (°C)-9-10-8-6-12552-2-6-8
Min (°F)77914232732322721149
Max (°F)161418213036414136282118

In the plains and at low altitude, spring and autumn are quite cold in the periods closer to winter: in March and in November it may freeze and snow: in November, record low temperatures go from -11 °C to -19 °C (-2 to 12 °F), and even -20 °C (-4 °F) in Innsbruck.
The situation is definitely better in the months of May and September, when the temperature is usually pleasant (although sometimes it can get cold at night), and thunderstorms occur more rarely than in summer. On warmer days, the temperature can reach or slightly exceed 30 °C (86 °F).
April and October are very cool, sometimes cold: in these months sometimes it can freeze at night, and in April the northerly winds may bring some late snowfalls.
In autumn, in October, mists and fogs become quite frequent.
Spring and autumn in Austria are drier than summer; in autumn, the north side of the Alps is sheltered from the southern winds which usually blow in this season, and bring heavy rains on the southern side, namely in Italy and Slovenia.

When to go

The best times to visit Vienna and the other major cities in Austria are late spring and early autumn, especially the months of May, June and September, because in mid-summer (July-August), thunderstorms are more intense, and in plains and low valleys there can be heat waves.
In hill cities (Salzburg, Innsbruck) it rains a lot more than in Vienna, which in return can be hot and muggy. After all, mid-summer is not a bad period, especially for those who can stand the heat.
Winter (December to February) is not the best period to visit cities, because it's cold and foggy, and sometimes freezing and snowy.

The best time for excursions in the mountains runs from mid-May to September, bearing in mind that in this season, especially in July and August, thunderstorms are frequent in the afternoon. September is quieter, and forests begin to show the spectacular autumn colours.

For skiing, the period of March and early April is preferable to mid-winter, because it's less cold and the days are longer. However, on high mountains there are resorts where you can ski even in summer.

What to pack

In winter: warm clothes, sweater or fleece, down jacket, hat, scarf, gloves, umbrella. For the mountains, mountain outfit, hiking boots.

In summer: light clothes, T-shirt and shorts, but also long pants, jacket and sweatshirt; raincoat or umbrella. For the mountains, hiking shoes, sunscreen and sunglasses; for the highest mountains and glaciers, warm clothes, down jacket, hat.