More on layering -- I did a ride recently where temps were in the low 40s at the start, with the sun obscured by clouds. I wore a long sleeved wool base layer and then two long sleeved cycling jerseys over it. Then I wore a windbreaker (snug fitting, so it doesn't puff up with air as I ride), with a sleeveless wind vest over that. None of the layers was at all heavy or fleecy or insulated. After 90 minutes or so the sun came out and things warmed up a bit, so I started to remove layers. I ended the ride wearing the wool top and one jersey, plus the vest.

Depending on the conditions, a short-sleeved jersey over a long-sleeved top or a tank top under a long-sleeved top can be comfortable. With layers, you can get double-duty out of clothes that you would normally wear in warmer temps.

You might find that you need an additional bike bag to help carry the layers as you remove them. I bought a small handlebar bag for this purpose.

For hands and feet, make sure your gloves/shoes/socks etc are not too tight. Restricting blood flow will make your extremities colder.