during last winter my transmission acted gerirattric.

Because you say it wouldn't shift I am going to assume you have an automatic.

What you were experiencing was called slippage. Slippage is a bad sign. It happens even more in extreme cold and hot weather, with some transmissions. The extremes make the problems amplified. In cold weather the fluid moves slow too. Did you check the fluid level? If you didn't check the transmission fluid you really need to. You can burn up a brand new transmission if it is low on fluid. If the fluid has a burned smell, and it is full, you have big trouble. Your transmission will have to be rebuilt, or replaced. I know this is not what you wanted to hear. There is very little you can do to an automatic transmission without removing it from the car.

I hope this helps, good luck, and Thanks.

can i check it myself? if so how?

There will be a dipstick under the hood of the car. It is a lot like an engine oil dipstick, but bigger. Once you find the dipstick, start your engine. Set your parking brake and place the transmission in Neutral. Now pull out the stick, wipe it off with a rag or paper towel. Reinsert it push it all the way in. Now pull it out and read the level on the end of the stick. It will tell you things like "high" "low" they may use other terms too. Also be sure the car is on level ground. If you need to add fluid, you place a funnel into the dipstick tube, and add fluid there.

I hope this helps, good luck and thanks.