It's because there are 2 types of adjectives in japanese i- adjectives and na- adjectives. Samui is an i-adjective, as it Ends with an i. So to form the past tense for i-adjectives you get rid of the last i and exchange it with katta, hence samukatta (desu). For na- adjectives like shizuka it is like you expected: shizuka deshita. I think you should look more closely at the past tense, because sadly reducing deshita to was is not that easily. I hope I was able to help.

It should be sumukatta, or samukatta desu. It was cold.

Yeah, what the original Answer said. One can say "Samui desu" in present tense, but one cannot say "Samui da". You could, but it would make you sound silly. Desu are added to i-adjectives only to make them sound polite. To a stranger you can say "Samui desu ne?" But to your bestfriend you'd just say "Samui ne?" since you don't have to add the desu to be polite. Now, with "Samukatta desu", you'd just say "Samukatta" in an informal situation.