I would like to visit Granada in January but also spend some some days Sking in the mountains.
It is possible to rent apartments in the Ski resort itself?
Click on this link.
It will take you to a page full of apartments to rent in the Sierra Nevada
https://booking.tpx.lt/qdugFQD1
Note that any accommodation in the Sierra Nevada is normally quite expensive.
If you don't mind driving up and down the mountain it can be much cheaper further down or even in Granada itself.
Frequently asked questions about Granada