[BerntR]

As Roald Amundsen said: Put on a cap if you freeze on your toes. It is not how much you put on your hands and arms that determines whether you'll have cold hands. It's how much you put on everywhere.

Here's my stock dressing for a very cold day at the course:

Long foot underwear
Some sort of thick gym trousers in the middle
Rain trousers on the top

Wool T shirt
Long sleeve polo
One thin "middle layer" wool sweater
Another sweater with an inbuilt wind breaker
Possibly a rain jacket on top.
A warm cap
A scarf

Key is to have plenty dressing on the large body parts. So that you get a little hot. This will keep the hands and arms plenty warm & smooth without using extra gloves etc. You can always remove a layer or two on the course if it gets too warm.

The rain jacket, the middle layer wool sweater, the cap and the scarf goes on and off as needed.

And ditch the cart. Walking keep you warm.