According to published figures (Scientific Publications Workshop Manual Series No64 Morris Austin Mini, Pg 224), standard mini oil capacities are:
Engine/transmission including filter 4.83 litres
With oil cooler 5.25 litres
I compared this on the weekend with an old oil cooler I had, and the above appears to be a pretty accurate measure.
This works out at 8% of your old oil not being changed if you don’t empty the oil cooler contents each time you do an oil change. If you happen to do low miles/kms between oil changes and your engine is in good condition, then I don’t really see any concerns. However if your oil gets pretty dirty between changes then it might be worth considering cleaning out the oil filter oil as well. Just think, after doing an oil change how would you feel about pouring 8% of your old black dirty oil back into the mix...?
My car is a '70 Cooper S which came out with an oil cooler as factory standard, so I’m going to keep running one and keep my car original. The engine has been recently fully rebuilt, and has a new oil cooler fitted. I’ve fitted some rare earth magnets to the oil filter and sump plug to assist with picking up any fine grit in the oil. Also, I don’t tend to do short shopping trips in my car, and so the engine always gets to full operating temperature for a decent amount of time in a generally warm climate (Sydney).
I reckon if I lived in a genuinely cold climate – England, or say Goulburn

– then then I might reconsider running an oil cooler. If your car didn't have one standard, then I really don't see too much benefit in running one unless your car was seriously highly tuned, or doing a lot of trackwork.
In the meantime I'll just make sure I do regular oil changes (Valvoline XLD Classic), and probably clean out the oil cooler oil every 2nd/3rd time.
Any further thoughts?