Thanks for the suggestions!
Switching equipment other than headgear underground currently costs 5 stamina, and for footwear specifically, changing them below the surface only affects max stamina, not your current amount. For example, if you're at 100/100 with Leather Boots and switch to Snowboots underground, you'd drop to 95/115.
Auto-switching also gets a bit complicated when multiple tools or footwear share similar bonuses in the future. For example, if two pickaxes both offer +3 Power, the system wouldn't necessarily know which one you'd prefer. So while I really like the idea in principle, it might need some careful design to avoid it becoming confusing or too automated in ways that take choice away from the player.
Still, I've made a note of this and will keep it in mind. It's always helpful to hear how all of you are playing and ways to make the game better, so thanks again! :)