I have always featured restoration in my builds in the past, but I am now doing a Nord Berserker who dual-wields axes whilst wearing fur armour (shirtless variant or just shirtless if I can't find any). Since Nords don't generally like magic and Berserkers are more warriors, it'd make more sense from an RP perspective to not use even restoration. However, will this prove difficult? What are the ingredients to find health potions and how difficult are they to find? With this in mind, what level should I play the game at?

I always have a huge, huge number of health potions on me that I never use. Surviving shouldn't be hard at all, especially if you remember to stock up on the potions whenever you visit a town.

Easy. Restoration really isn't that useful when you're severely outmatched in a fight, anyway. Just keep a healthy stock of potions.

First question: yes, it's difficult, especially since you're not using strong armor. I'd suggest finding at least one axe (and maybe both) with a strong vampiric drain effect (to replace lost HP), and using either the Whirlwind Sprint shout (to get into fighting range fast) or the Ethereal shout (to be invulnerable while closing). And devote most of your level-ups to health (a few to stamina for power attacks). Finally, don't be afraid to flee from combat if you're overmatched.

Second question: For ingredient effects, look here: http://elderscrolls.wikia.com/wiki/Ingredients_(Skyrim)

Restore health potions can be easily made with very common ingredients: combine any Imp Stool, Butterfly Wing, Blue Mountain Flower, or Wheat.
Most of my current characters use Restoration because I like it so much, but I've played without it before (an alchemy-skilled character).

Restoration is useless unless fighting the undead.

You find so many of those Extreme and Ultimate level health potions that you never have to use the skill to heal yourself.