So basically it means ' likes/yearns for the transitions into winter and summer and the seasons themselves?' (I understand the nuance but I can't think of a perfect-fit translation at the moment for koishiku.)
It's more likely "fuyu ni naru to" "natsu ga koishiku narimasu". To parse "fuyu" "ni naru to" doesn't make much sense. (Nekojita-san just explained about a structure ~になると.)
It's "koishiku narimasu", not "koishiku ni narimasu", by the way.