Suggest first upgrade/ Maintenance?

[jonsi7777]

Hello mini people, I currently have some time on my hands and would love to improve the life of my little 1275 mini and my skills as a beginner in car mechanics. 

It runs well, although struggles to start on these cold winter days (which I assume is normal ==> I am very new to this mechanic lifestyle). So I was asking for some guidance from you mini-experts on what would be a good thing to invest some time into, be it some routine maintenance or a suggestion to what systems or components need specific love/ upgrading. I have noticed that the wiring in the car seems a bit messy and the hoses old, I would love to replace them but It feels quite hard to do anything without removing the engine, which do you think is a manageable task for a beginner, or is it not worth doing if the car is currently running? I am a 3rd-year electrical engineering student, so I do have a basic understanding of electronics and mechanics. I do have a Haynes manual, so instructions seem very clear.

Thanks so much, can't wait to learn more! Just replaced the headlights and 4th spark plug (which appeared oily -> maybe some work to be done there?)