How difficult would it be to use a character with heavy armour, who uses a bow at range so needs the sneak bonus? I wouldn't be using sneak once close, it would just be melee then.

Not all that difficult, I do this.

As long as you're far away and don't make noises, you won't be found.

Movement might be more noticable though.

I agree. If you're talking about ducking into Sneak temporarily to get a sneak bonus from Archery, I don't think it will matter what kind of armor you're wearing.

Easy. Steed stone and muffle is like you have no armor at all

Edit: muffle spell is what you want. Enchantment is hard to find. Casting the spell takes no perks in illusion.