A good windshield keeps the cold windblast off you, so for sure you'll stay a little warmer. YOu don't have to fight the wind to hold on (you don't realize you're doing this till you try a shield...) so it's easier to ride longer. Size it so you're the top of the shield is a couple of inches below your line of sight. I like to look over it rather than through. For the most part the shield directs rain up and over your head - it's much better then without.
Before I got my '00 Standard when I toured some on the FXB, I would put the stock length shocks back on, a set of throw over bags, a big puffy seat, the mid mount pegs (I put forward controls on the bike), and a big hideous HD removable shield. An FXBTC, if you will

It looked like hell but it was a lot more functional. The shield makes a huge difference.
Hmm, I guess all i need to say was yes, you'll stay warmer and it's way better in the rain...
You may want to give a full face helmet with a balaclava underneath a try too, it's way better than an open face (or none) in cold/wet.