It’s a bit hard to translate into English, I think. The first word, 冬眠, combines 冬 (winter) and 眠 (sleep). So, “winter sleep” is what we call “hibernation” (noun) in English. Being a noun, the verb form is created by appending する, creating 冬眠する. And this refers to any animal that sleeps during the winter (hibernation).
冬ごもり combines 冬 (winter) and こもり (to shut oneself in (e.g. one’s room); to be confined in; to seclude oneself; to hide away). As far as I can tell, this refers only (mostly?) to bears. (This Weblio page doesn’t specify bears, but it does say 冬ごもり is different from 冬眠, and close to sleep.)
So, I read it (not direct translation) as “Precisely, bear hibernation.”
While looking for something more definite, I found this Japanese blog post which says (with as best I can translate):