Just did a Mosin yesterday, and the following worked really well...
Completely dis-assembled the rifle (including dismantling the bolt assembly, which is dead easy on a mosin and most Soviet guns).
1. Put all the small parts in a bucket with enough Mineral Spirits for everything to be submerged.
2. Hung the stock and handguard a few feet from a propane powered heater (still a little chilly in the garage).
3. Soaked a rag in the mineral spirits the small parts were soaking in. Used that to start wiping down/scrubbing the barrelled action. Ran some patches soaked in mineral spirits through the bore, let that soak in, ran a bore brush through the bore, ran one more soaked patch through then dry patches to get the last of the spirits out. Wiped the whole thing down with a dry rag to remove excess mineral spirits. (sounds complicated but really only took about 15 minutes).
4. Wiped the cosmo that was starting to sweat out of the stock with a rag. Left hanging in front of the space heater again.
5. Started pulling the small bits out of the Mineral Spirit soak. Most of the cosmo had dissolved off by this point, scrubbed and dried as appropriate. Another 15-20 minutes.
6. Wiped more cosmo that had sweat out of the stock with a rag. Left hanging in front of the space heater again.
7. Went through a normal clean and lube process of all the metal parts and barrelled action. Re-assembled the bolt and set it and all the other parts aside.
8. Wiped down the stock again, not much any cosmo had sweated out this time around, calling it done.
9. Re-assemble everything. Gave it a quick wipe down with a rag that has gotten "damp" with lube over the years.
10. Threw it in the safe.
Sounds like a lot of work, but it really wasn't. Took about an hour total, and everything is thoroughly de-cosmofied, cleaned, and lubed. Looks pretty much new from the factory at this point, aside from some very light normal wear on the stock - got a real gem from Corwin a month or so ago, just hadn't had a good weather day and the time to get to the garage and clean it up.
Mineral spirits are a reasonably gentle solvent, and don't give me a headache like some of the other solvents out there. Brake Cleaner is way more powerful, faster, and in an enclosed space, you can get a pretty good buzz on - not my thing, but hey, some people enjoy sniffing fumes.
Gentle heat on the stock is less likely to cause the original finish to peal off than a chemical treatment or even steam. Steaming can work, but you have to be careful - some people overdo it and end up taking a lot of the finish off. Up to you, go with what you feel confident doing.
Everyone has their own recipe. Mix and match and go with what works for you.