A thin short sleeved shirt under pads is best. Sweat shirts under pads is bulky and hard to wear. Long sleeve shirts tend to get tangled in arm pads, but if you have a thin one, it might work.
Put on a big sweat shirt over should pads. The looser the better.
Sweat Pants are great to have. Heavier and Bulkier are better in this weather. This is one area you can bundle up and not effect your childs ability to throw or catch. Keep the legs warm !
Hands are the toughest part. You can try very thin baseball gloves under the lax gloves. You can tape the stick with athletic tape so his hands are not touching metal directly. I have tape at practice, or you can do it before hand. Cold hands is by far the worst for the child, and unfortunately there is no great solution.
Thin or Medium wool socks are great. Do not use thick socks that constrict the feet, thus reducing blood flow and warmth. Wool socks maintain warmth even when wet. SmartWool makes good athletic socks.
Hydration is just as important in cold weather as in warm weather. Hydrate before practice. Eat something so the body has calories to burn in order to generate heat.
Have some hand warmers in your kid’s bag for game days.