[inglor_cz]

Pre-industrial holes may collapse long before you reach -100 meters. Even -5 meters is a challenge in certain places.

Also, digging (or rather drilling) in bedrock is hard without motorized equipment and good steel.

Also, supplying fresh air down there is a problem.

Also, preventing the mine from flooding is usually a huge problem.

Mining is hard and a lot of people lost their lives doing that. That said, if your only intent is to get a bit warmer, you may basically try a good cave. Caves tend to have temperatures above freezing for the whole year.

[nervousvarun]

And of course the difficulty with caves is hibernating predator(s) (bear is the one I can think of maybe more?)

[inglor_cz]

And lions:

https://en.wikipedia.org/wiki/Panthera_spelaea

IDK if these lions hibernated, but their bones are definitely found in caves all over Europe. Often with human remains or artifacts nearby.