I have an '07 Cooper S, and the windshield washer doesn't squirt a whole lot of fluid onto the glass. This started on my first cold weather trip, so originally I thought the fluid froze in the line, but the issue has continued ever since (even in warm Southern California).

I have not found any leaks, and the reservoir has plenty of fluid. Where is the washer pump located, and can it be seen/inspected without taking half the car apart?

 

Could be there is detailing wax buildup in the washer nozzles.

Use a fine sewing needle and see if clearing them out helps...

 

You could re-name your car little-squirt!!!
Lol. I'd bet 5$ there might be wax or a piece of junk in the nozele....a needle to try to poke it out is a great first step in trouble shooting....then look at the hoses on the back side of the hood...look for kinks....heck even unplug the sprayer and check for volume/leake /psi....
All else fails...you are down to a new pump....
Pretty simple diy stuff to look at/check! Good luck!