I haven't recipes with leather at the Spinning Wheel, how can I get them? I've found some planet where I can be 15 seconds at the most.
You can use campfires to warm up on frozen planets. Just keep one in your toolbar and you should be fine. Nights seem warmer on frozen planets, so you might want to go on adventure at night and stay at camp during day time.
The gear you're looking for in the spinning wheel (Yarn Spinner) is called Snow Infantry gear.
I tried exploring a snow/frozen planet and put down a camp fire right away. This did keep me warm as long as I stayed within a few blocks of it. Once I started wandering away, my body temperature began to fall rapidly, but soon after I got a notification saying a new blueprint was added.
I returned to my ship and looked for the new recipe in my Crafting Table and anvil, but did not see it. So I crafted the Yarn Spinner and saw that I now had recipes for the Snow Armor. This currently has similar armor stats to the silver armor and since it uses leather I found this an easier way to up my armor. I initially had only enough leather for the headpiece and boots, but that was enough to keep my body temperature up as I explored.
Since they are doing a lot of updates this may change soon, but I would try wandering a little ways away and see if it comes up if you do not currently have the recipes.
It may be hard to get enough leather for the snow armor (it is for me), so I suggest the way to do it is to teleport down, find a safe short cave that goes down a bit, and put down some torches in a 2x1 space, it definetely works for me. P.S. this also worked on a moon, one of the coldest planet types