1996 Volkswagen Jetta Rear Suspension/Strut

I believe my Passenger Rear suspension/strut has gone bad. It started about two weeks ago when the weather dipped below freezing. I would go over the littlest of bumps, even small cracks in the road and I would get a big thud out of the rear tire area. I assumed it was a bad strut. Which I do believe is what my car has. I went and priced them last week but couldn't order them until earlier this week due to thanksgiving(no one had them in stock) So I decided to wait and order them this week. About 2 days later as the weather warmed I noticed that the sound became less and less pronounce, until eventually it was completely gone. No big thud even over railroad tracks whatsoever went well for the whole week, until today. The weather went cold again last night and the thud is back. Do I have water in them that freezes? Are they bad? And Are my suspicions correct? I have checked over the owners manual nothing about whether it's a strut or a shock, it has a coil so I assume it's a strut. Is it an easy fix? And what tools will I need in order to fix it?