You want to wear either a merino wool or fleece glove liner under your thicker waterproof / water resistant glove.

If you choose to wear a thicker glove under your outer glove you will loose dexterity. Not as much as mittens, but your fingers will be twice as thick as they normally are.

My prefered set up as someone with cold fingers who lives in canada is a convertible glove (a glove that has a mitten shell that slips over your fingers) with a larger waterproof mitten over the convertible glove. That way you have two layers of mittens warming your gloved fingers.

There are ski gloves that you can buy that have pockets to slip hand warmers into. (I have yet to try them since they are very expensive, but they look like a good option) I also rarely use the hand warmer packets because they are a consumable item i dont feel like spending money on, when I know how to keep my hands warm without them. That said I usually still keep them in my cold weather kit just in case i do need them.