In reply to Oli_31: February wont be too late. If its anything like last february , temps were down to -25 in Zakopane in the day...making climbing up high a challenge!
There was also alot of snow last year , making getting to the base of the walls almost impossible without skis...but this was an exceptionally strong winter.
The main areas on the polish side are Hala Gasienicowa and Morskie oko , the later having one of the biggest walls in the Tatras.
Both have really nice huts , see links below.
If you stay in Zakopane as your base , expect long approach's (2.5/3 hrs normal in winter)
Morskie oko hut to climbing(30mins), Gasiencowa hut to climbing(1/1.5hrs)
If you stay at Morskie oko , they have a climbers hut behind the main hut thats cheaper(same booking number)
The closer stuff to Zakopane is the west Tatras , but its banned as its a nature reserve.
Around 30mins from Zakopane is Dolina Bialej woda , its a good waterfall ice area( the closest easy access area...well that your allowed to go to anyway)
If there is too much snow , at least you have good skiing( if you dont ski its a cheap place to learn)
Any more info your after just message me ,glad to help.
Chris
http://taternik.net/
http://supertopo.pl/
http://www.schroniskomorskieoko.pl/index.html
http://www.murowaniec.e-tatry.pl/index_en.php
http://www.lodospady.pl/