Sneak & Archery for hunting ONLY?

I'm wondering if anyone has played as a character where you only use stealth and archery for hunting animals in the wild (for meat,pelts, ingredients for selling and crafting or whatever) but when it comes to fighting enemies like bandits, soldiers, mages and draugr, you face them out in the open without sneaking or shooting from the shadows?

It seems like the sort of thing a warrior living in an environment like Skyrim might do - when you're hunting you're doing it for survival, but when it comes to fighting enemies you're proving your strength and skill in battle rather than playing an assassin killing people before they even notice you (making the battle one sided). But it might make for a jarring game play experience, because if I'm sneaking around shooting deer in the forest, it's likely to get me in the habit of wanting to sneak around and shoot enemies from afar.

How do you feel about playing like this?

How do I feel about playing like that? Indifferent. It's one of many role-play styles (if you're willing to look at it like that).
After reading your post I had a few flashbacks, and I must say I've done same thing myself, BUT rather unintentionally. I see a deer, crouch, and take it out with arrow sneak attack. Main purpose of crouching being saving the arrows up, not as role-playing or anything. Though, most of the time, I just run past them.

I may do that with my nord, who is likely to be a barbarian. My only issue is that I would have to add a camping mod and hunterborn, just for Roleplay.

I've been doing it with my spellsword. So when he enters a lair of bandits he doesn't sneak around trying to kill them before they notice him, he'll confront them out in the open blasting them with spells and hacking them down with his sword. But when he's traveling through woodland and hills, he'll sneak and use his bow to kill wild animals and make use of their remains, either for food or crafting potions and armour. He'll also use his bow to shoot dragons when his magicka runs low.

This sounds like a really cool idea!

In fact, I'm just about to start playing Skyrim again, and re-create my old HA, 2-H Khajiit character. He would work perfectly with this kind of playstyle -- and it'd give me extra skills to use on a regular basis.