I want to try to be a nomad for as more days as I can, playing in hardcore mode. What difficulties will I encounter with this strategy, compared to a more traditional approach of establishing a base?
You cannot keep stuff in chests, so you'll have to optimise your inventory. Keep resources in their densest form, e.g. Logs, Iron blocks, Gold blocks. Throw away excess stuff when it's time to move, only take your most valuable (irreplaceable) stuff with you.
You'll probably want to establish a temporary base while you mine. It's not worth keeping anything but the end product so smelt and 'compress' everything while you move on.
You won't be able to farm any food, so kill every mob you see for food.
Always have enough basic blocks (wood/dirt) to construct a minimal shelter, and always have a bed so you can skip the night.
Always keep a crafting table in your inventory.
Since it's hardcore, always have a weapon, and build leather/iron armour as soon as possible.
Try and skip nights as often as possible. Only travel during the day.