My first thought was snug as a bug in a rug, but @WS2 beat me to it in his answer, and @Phil Sweet had a super reference in his comment. So I will point out that snuggly is a familiar word and warm and snuggly a familiar phrase.
From Oxford Living Dictionaries
Comfortable, warm, and cosy.
‘she had to stay in her snuggly bed until the last second’
a snuggly pair of slippers.
As for warm and snuggly:
The power failure did not bother us, because we were warm and snuggly,
wrapped in blankets in front of the wood stove. (Made up, based on personal experience.)
See also images for warm and snuggly
For the many meanings of snug, see the OED. You may be amazed, as I was, to find the winter climate of Duluth described as snug in a quotation from 1888.
Addendum: The OP may have confused snugly with snuggly -- or he/she may have made a typo. Anyway, from Oxford Living Dictionaries
Snuggly and snugly are quite different in meaning, though frequently
confused. Snuggly is an adjective meaning 'comfortable, warm, and
cosy', as in a snuggly pair of slippers. Snugly is an adverb meaning
'in a very tight or close-fitting way', as in the ring fit snugly on