Map from Google - Slovakia

In Slovakia the climate is moderately continental in the plains, and it becomes colder with increasing altitude in the mountainous areas. The west (see Bratislava, Nitra) is flat, in the north there's the vast mountainous region of the Tatra Mountains, while the rest of the country is covered by hills and low mountains, belonging (like the same Tatras), to the vast region of the Carpathians.
In the western part of Slovakia, where the capital Bratislava is located, the climate is moderately continental, with cold winters and warm summers. Precipitation is fairly frequent throughout the year, but it's most abundant in late spring and summer, when it can occur in the form of thunderstorm, while in winter it often takes place in the form of light snow.
Here is the average precipitation in Bratislava.
Average precipitation - Bratislava
BratislavaJanFebMarAprMayJunJulAugSepOctNovDecYear
BratislavaJFMAMJJASONDY
Prec. (mm)403535405560505050355050555
Prec.(in)1.61.41.41.62.22.42221.42221.9
Days141213111112111110101415144

The daily average temperatures in winter are around freezing (0 °C or 32 °F), while in summer they are around 13/15 °C (55/59 °F) at night, and 25/27 °C (77/81 °F) during the day. During winter, the area of Bratislava can experience dull and wet days, but also intense frosts during the outbreaks of cold air from the east, in which the temperature can drop to -20 °C (-4 °F), while in summer sometimes it can experience muggy days, when southern air masses prevail, with peaks of 30/35 °C (86/95 °F).
Here are the average temperatures of Bratislava.
Average temperatures - Bratislava
BratislavaJanFebMarAprMayJunJulAugSepOctNovDec
BratislavaJFMAMJJASOND
Min (°C)-4-215101315151161-2
Max (°C)25111622252727221584
Min (°F)252834415055595952433428
Max (°F)364152617277818172594639

Most places throughout the east-central of the country are located at a few hundred metres of altitude: just enough to make the climate slightly colder than in Bratislava, so that the snow remains on the ground more easily during winter, while in summer, the heat, when present, is more bearable.
Here are the average temperatures of Poprad, located at 700 metres (2,300 feet) above sea level:
Average temperatures - Poprad
PopradJanFebMarAprMayJunJulAugSepOctNovDec
PopradJFMAMJJASOND
Min (°C)-8-7-315810962-3-7
Max (°C)0271217202222181351
Min (°F)181927344146504843362719
Max (°F)323645546368727264554134

In the far east, east of Kosice, there is another small flat region, where the climate has the typical continental characteristics of Eastern Europe: colder winters than in the capital, with longer periods below freezing even during the day and weak but frequent snowfalls, and warm summers, with frequent sunshine but also fairly frequent afternoon thunderstorms.

The mountainous areas of Slovakia have a colder climate due to the altitude, especially the northern part, where the Tatra Mountains are located. Here the climate is cold and snowy in winter, mild or warm with afternoon thunderstorms in summer. In addition, the wind is more frequent. At 2,000 metres (6,500 feet) above sea level, the average temperature is around -8 °C (18 °F) in January, and 6/7 °C (43/45 °F) in July.
On top of Peak Lomnický, at 2,634 metres of altitude, it's cold and it can snow even in summer. Here are the average temperatures.
Average temperatures - Lomnicky stit
Lomnicky stitJanFebMarAprMayJunJulAugSepOctNovDec
Lomnicky stitJFMAMJJASOND
Min (°C)-12-13-10-8-30110-3-8-11
Max (°C)-8-8-6-3135630-4-7
Min (°F)10914182732343432271812
Max (°F)181821273437414337322519

When to go

The best time to visit Slovakia runs from mid-May to mid-September. In the period from July to August, hot and muggy days may occur, especially in the lowlands (region of Bratislava and the easternmost plain), while in the rest of the country the nights remain cool even in the hottest periods. In plains and valleys, during the warmer months the rains occur often in the form of short thunderstorms, that do not reduce too much the hours of sunshine. In the mountains the cloud cover in the afternoon is more frequent.

What to pack

In winter: warm clothes, sweater, down jacket, hat, gloves, scarf.
In summer: light clothes, T-shirts and shorts, but also long pants, jacket and sweater for the evening or cooler days; raincoat or umbrella; for the mountains, warmer clothes depending on altitude, hiking shoes and sunglasses.