"warm and comfortable," 1882, from toast (n.1) + -y (2). Related: Toastiness.
Entries linking to toasty
toast n.1
"piece of bread browned by fire or dry heat," early 15c., from toast (v.1); originally as something added to wine, ale, etc. From 17c. in the modern sense as something eaten on its own with a spread. Slang meaning "a goner, person or thing already doomed or destroyed" is recorded by 1987, perhaps from notion of computer circuits being "fried," and with unconscious echoes of earlier figurative phrase to be had on toast (1886) "to be served up for eating." But other sources claim the extended sense and popularity is from the 1984 film "Ghostbusters."
-y 2
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.