Summer and winter take the -n ending with appropriate linking vowel, as if you were saying "on" summer and "on" winter: nyáron and télen
Spring and autumn take the -val/-vel ending (which isn't explained as a topic on Duo), as if you were saying "with spring" and "with autumn." The v of this ending assimilates with other consonants, so you get
ősz + vel = ősszel "in autumn"
tavasz + val = tavasszal "in spring"