calpopscalum, we've only travelled in Poland from May onwards, and the weather at the beginning of May is just starting to warm up, so I'd imagine March would still be cold, although I've got not experienc of it myself.
As far as travelling to Auschwitz is concerned, the easiest way is by train from Krakow station. You need to train going to Oswiecim, the Polish name for the town. It takes about 50mins, and you then take a bus from outside the station to the museum - it's about 5 stops. The museum itself is mainly in the camp called Auschwitz, where many of the buildings contain lots of information, photographs and artefacts. A lot of it is understandably upsetting. You are asked to behave in a respectful manner when visiting, and it's best not to take 'this is me at Auschwitz' type of pictures by the gate or in the gas chambers, which we saw some tourists doing, and found rather tasteless.
The Birkenau part of the camp is around 5 times the size and has been left in it's original state. I believe there is a shuttle to it from the Auschwitz museum - we didn't actually go there, but my fil visited Birkenau, and the pictures show lots of barracks, some of them ruined, the railway entrance to the camp, the original latrines, bunks and washing areas.
I don't know what your expectations are of the place, but you'll certainly find it educational.