Ukraine is a great country. I was in Ivano Frankovsk and in Harkov - amazing places. At this moment I don't think that Ukraine is very safe place, but not so dangerous as Russia. I hope that next winter I will visit Bukovel with my Ukranian friends.
Check Dragobrat also. Great for freeride and backcountry, definitively have its own spirit. Old lifts but really great mountains and lot's of snow.
http://www.dragobrat.ws/uk/This is the first time I am hearing about Dragobrat, so I researched about it a little bit. It is located within the Zakarpatska oblast, near the Hungarian border. Not a very famous resort, but it is quite popular with those from the ex-USSR states. Don't know whether the Ukrainian government is having the resources to develop this resort.