what clothes do i pack to the hospital?

for christmas i told a lot of people i didn’t want anything for me, and that i just wanted things for our baby, who is due in May. we got a lot of clothes for our little girl! and we’re very grateful. but a lot of the newborn and 0-3M clothes are long sleeves. we live in Oklahoma, where we start to feel the heat of hell between March and April, so by May, we’re pretty much boiling. i know that babies being “too warm” can increase the risk of SIDS so i want to be very cautious about that. would it be a bad idea to dress our newborn in longlseeves when it’s hot outside? or would it not be a big deal? i don’t want the clothes our family got to go to waste, but i also want to be extra safe!