How to get up in the morning when it's cold and you're exhausted

Winter is here and heating has to be moderately low overnight or the air dries out and we all wake up with a headache.

I've been trying to make sure I switch off the lights by 22h30 every night (which I've so far done for 12 nights in a row) but am still battling the usual insomnia that keeps me awake past midnight. Result = I'm always exhausted when I wake up in the morning.

There are lots of things to be done for better sleep (as per this repo), but what can be done when you've already woken up and you're exhausted to help you cope? (Both practical tips and 'one must have a plan' type tips very welcome!)