My pal uses a 70s Mini on a daily basis- and that includes through the winter too. I honestly don't know how he can tolerate it. Poor wipers, poor ventilation, misted up windscreen, ice on the insides, locks frozen... yadda yadda yadda!
The silly thing is, we did of course use these cars all year round, it is possible and I have always enjoyed reliability on all of my Minis. The difference is nowadays, a modern car is such a massive leap forward in usability. The comfort, safety, performance and security is a million times better, even on, for example, a £300 Astra or Focus! There's just no need to put a classic Mini through the rigmarole of everyday use when something (much) cheaper will do the job much better in every single way.
OP, I have had a 1976 Mini for many years. I use it any day of the year apart from when there's salt on the roads. But... I'd never want to rely on it. It's a fun toy for an evening blast through the lanes, or a weekend's trip to the pub with friends. Having said that, I sometimes commute in it during the summer months. I shudder at the thought of using it as something that I'd have to rely upon.
The early Minis, up to 1976 are not easy to live with. They have solidly-mounted subframes, which bless the car with amazingly responsive steering, but also transmit a lot of noise and vibration through the cabin. They have drum brakes (unless you have a sporty one!) which are only just up to modern motoring and need regular adjustment. They have seats which don't adjust or support your back. Just a couple of things that would eventually be changed in the mid 1980s onwards.
A later car is much better, eg disc brakes, better seats, more insulation but still no match for your £300 modern banger!
Definitely go for a 70s Mini, I love mine and it really does put you back to a simpler time, but you'll grow to hate it as your only form of transport...