Hi New Owner: Getting many layers of old paint off of window sashes, jams, sills, stools and aprons is one of life's greater challanges :-)
When I redid all of my windows, I started by trying to strip the paint with everything (except the window casings) in place.....not good. I wound up very carefully prying off all the pieces to include actually taking the windows out and doing them on the shop bench...much, much easier. Some of the pieces I just ended up replacing, by making new pieces out of straight grained, kiln dried pine or doug fir.
If perchance, you don't want to go to this much work, you can remove most of the paint using a product called (I think) 'Strip EZE' or 'Strip Away', which consists of paint stripping gel on thick paper that you apply to the paint surface, let set and peel off, taking most of the old paint with it. Another way is to use a heat gun, being careful not to burn or char the wood or crack the window glass.