Most folks come up here in June or July. But if you want the BEST chances of seeing Denali come in April or May.
Yes it is a bit cool, days are in the high 40's to low 50's here in Fairbanks but skies are very clear, free of pollution and this is still a very dry time (fewer clouds).
So if you are planning to come this JUNE start now if you can. If you are planning for next year same thing. And you have the added benefit that things are not nearly as crowded and busy.
By the middle of May virtually everything is open.