Cold weather preparation
How cold one can ride safely and comfortably all depends on preparation. Once you get down below the 60's, riding for any length of time and at speed requires some preparation to stay comfortable and avoid hypothermia. Riding on the highway for extended periods is a very passive activity. While 20F is not so cold on a ski slope, moving at 60 mph produces a wind chill of -4 and a frostbite time of only about 30 minutes.
One simple thing you can do is to get geared up before you leave the house/truck stop. Having your gloves or helmet off for any reason outdoors lets a bunch of precious heat escape.
If you can't stop shaking (despite warm gear, etc...) you need to stop somewhere warm. You are not only dangerously distracted, but your body is trying to tell you something by attempting non-stop to generate heat. Hypothermia can be life-threatening!
Also, people forget that they need to drink just as many fluids as when it's hot out. Cold, dry air = dehydration. Drink up and avoid too much caffeine (which will act as a diuretic and cause you more fluid loss).
Your hands may be the first thing to feel cold, but rather than starting with this symptom, you should take a look at the big picture.
If your core (torso) is cold, it will divert blood from the extremities (hands and feet). As counterintuitive as it might seem, don't start with where you feel the cold. Begin by addressing the core temp, and then work on the hands. The best thing you can do to begin is to get as much wind off you as possible. A good windshield is a great place to start. Get the wind off you and whatever clothing you are using will be far more effective.
A stout, windproof outer layer is vital. A good jacket and pants will cover most of you, but if you ride in colder weather you will also need to make sure to cover the areas where you can lose your warmth. You can 'leak' a fair amount of heat from these areas, and over a longer ride that can make you much colder. These are the main problem areas:
Layering is always a good strategy. Include a thin layer next to the skin (silk, polypropylene, UnderArmor (Cold Gear), Damart, etc...) You don't need to be bundled up with so many layers that you can't move, and you don't need expensive gear. Fleece can be an inexpensive and versatile middle layer. Silk works very well for the bottom layer.
Winter gloves can give warmth but can also add bulk and reduce dexterity. Some sort of hand guards to get the wind off your hands can really help. Hippo Hands and generic handlebar mitts aren't generally considered great-looking, but people who use them usually swear by them for the warmth that they add by getting the wind off your hands, rather than having the wind aggressively strip it away. It also allows you to keep a small pocket that is warmer than the ambient temperature. Mittens can be very warm, but at the expense of dexterity; it can be hard to keep a couple of fingers on the brake lever in mittens. Thin silk or polypro glove liners can add warmth without excessive bulk.
For rain riding, and also to help cut the cold coming from the wind on your hands, consider using your normal gloves and adding a layer over the top. The cheapest are latex or nitrile gloves, or regular old rubber gloves from a grocery or hardware store. You can also go to Aerostich and get their Triple Digit Rain Covers. You may also like neoprene kayak paddler's gloves under your armored gloves. Your hands don't stay completely dry, but warm and comfortable. Look at REI or NRS.
Heated grips, vests, gloves, socks, and the like are all available for motorcyclists. See this article. Given the electrical limits of the 250, you most likely won't be able to run all of those, but even just one or two of them can make a difference.
Heated grips generally get good reviews from those who install them. Heated vests can add warmth back to your core. Some say it is like riding in 10 or 15 degree warmer temps. If you only need a little more edge, many swear by their heated gear.
If you are going to seriously ride in the winter, you may well encounter one of the banes of cold weather riding: visor fogging (or, in really cold riding, frosting). Simply cracking the visor open is the simplest solution, but it does cost you some heat. Also, if you have clunky gloves or floppy generic handlebar mitts, it may not be as easy to fiddle with things on the fly as in lightweight summer gear. Many solutions exist.