So of course there are multiple ways to say anything in any language here are just the way I would say it. I'm not fluent I Japanese so there may be better ways but these will work
1. Translating these sentences literally
I am going to the store お店に行きます。
I went to the store お店に行きました。
You can also use the word 買い物 with する to say you went shopping
I'm going shopping 買い物します。
I went shopping 買い物しました。
2. Here are the ways I would translate your sentences
I love eating ramen, but only in the winter.
ラメンを食べるのが大好きですが、冬しか食べません。(I love eating ramen, but aside from winter I don't eat it)
I would exercise, but I'm tired
運動したいけど、ちょっと疲れた。(I want to exercise, but I'm kind of tired )