Speaking as a former diver and cyclist....
Neoprene IS waterproof. BUT, the difference between a wetsuit and a drysuit (made from Neoprene) are the seals. Drysuits come with either latex wrist and neck seals or neoprene seals. With neoprene, one side of the neoprene has no woven material, where the side without material bonded to it, designed to sit against the skin. Wetsuits don't have seals, simple.
Neoprene wetsuits work by allowing water in which the body warms up. The neoprene then prevents the heat escaping out of the suit. In a drysuit, the wearer has a thermal dry layer on under the drysuit, like wither a type of fleece (Arctic) or an insulator like Thinsulate.
I don't think neoprene would work well, as you would sweat inside, which would then cool. Also the material would likely chafe! Plus 3mm is not that thick. Traditional thermal insulation works by trapping air which the body heats.
I have neoprene gloves, (both 3 & 5mm) & mitts. Non of them are as good as traditional thermal water resistant gloves. The best skull cap I have is this:
https://life.fourthelement.com/product/xerotherm-beanie-hat-black/I have had it for ~15 years and it is still the best hat I own!!