Pylypets ski resort
A mid-2000s snapshot. Pylypets was then an up-and-coming ski area 12 km to the south of the Volovets train station on the Kyiv-Uzhhorod train line. The ski lifts (tows, actually) were new, and there had been a lot of construction there recently. For example, some cottages had been built near the top of the new ski run, which rose to nearly 1200 m above sea level from a base of 800 m.
You could get there by taking a 2 km walk or sled ride from the center of Podobovets or by taking the taxi another 7 km or so around the mountains (approx. 18 km total from the Volovets train station where the taxis were).
Here is a map of the mountain from skitours.com.ua (a period source for this guide; no live embed). In addition to what is on this map there was another lift to the left about the same length. Ski rental was available both at the bottom of the slope and in the nearby village of Pylypets.
In addition, one of the prettiest waterfalls in the Carpathians - Shypit - is just a 3 km hike from the bottom of the mountain. The trail was well packed in the winter and very easy to follow. The waterfall is quite dramatic in winter when it turns to ice.
skiukraine.info then offered help booking accommodations in Pylypets through a general form on the site (the page later became unavailable).
Source note from that period: skiukraine.info (the site later became unavailable).