If you get a new wheel/cassette, you may also need to adjust the rear derailleur from wheel to wheel. The new wheelset on my road bike required this, going from cheap factory supplied hubs to Shimano.
Personally, I would not worry about it until next winter. Its going to be riding weather outdoors now. Of course, I have an exercise bike so... Just use the tire you have now, if it wears some, get a new one for pavement, and get a trainer tire for next year!
Remember to order tires from PBK (Probikekit) in UK. Their prices on tires are just about unbeatable!