how should mitts fit?

Like any part of your body that requires circulation cramped is not better. Tight boot/sock combinations and tight gloves/mitts will lead to cold digits. Try different brand or split finger mitts like toko or pearl izumis to get a snug but not tight fit, also pay attention to how tight the elastic is around your wrists. You can use a light liner inside a mitt to take up the difference. Rent a copy of the Eiger Sanction and watch Clint Eastwood pull his Dachstein mitts off every time he clips in or places an ice screw in an ice storm, do not do this as you and the pro will become one.

Mittens should be pretty loose but not grossly so. One big reason is that it is hard to put on or take off tight mittens with cold fingers anyway.

You might want to try a different brand, because your hands might be just between two sizes. I almost always wear liner gloves inside my mittens anyway, so the extra size is even more valuable.

It’s not that the mitt is tight, it’s just that I can’t stretch my fingers outward inside the mitt which is sort of a wierd feeling being used to wearing gloves all the time. Is that just normal in wearing mitts?

This might be why you’ld like a lobster claw or split finger style, a mitten is basically made to curl around something and you shouldn’t be able to spread your fingers much.