You can use "animali invernali" or "dell'inverno" "Vediamo diversi animali invernali" "Vediamo diversi animali dell'inverno" Both the sentences mean "we see different kinds of winter animals" but the first sentence is the most used and of course the more advisable, while the second one sound unusual or strange because stress the winter and means something like "the winter's animals".
"Different" and "various" would make the sentence mean two different things -
"We see different animals in winter." = The animals we see in winter are different from the animals we see at other times.
"We see various animals in winter." = There are a number of different animals that we see in winter.
I don't know if "diversi" could include both those meanings. Can any native Italian speakers chime in?