The typical tool belt that...
The typical tool belt that you use in the summer months will work fine. It's always important to keep a screwdriver in your tool bag to chip away ice build-up on your foot pegs and rear brake lever.
Clothing
There are a handful of clothing manufacturers that produce good-quality riding gear for the winter. I prefer the Moose Monarch Pass jacket and pants, but MSR, Klim and others have great products as well. The jacket should be big enough to cover a couple of layers of clothes, have vents and enough pockets to store extra gloves, clothes and a stocking cap to wear during breaks.
The pants must be roomy enough to allow maneuverability, fit over boots, and keep the snow out. They should also possess extra pockets to hide your ID, cash, and snacks. I typically wear fleece pants under.
I've found the best way to keep my feet warm is to use a pair of Alpinestar Tech 8 (or others with a separate booty that is not part of the boot's support) boots with the liner removed. I wear polypropylene socks against my skin, a normal riding sock over that and a waterproof Gore-Tex sock on top. With the inner booty removed, it allows for more breathable room in the boot and ultimately more warmth with the layered socks.
MSR
Moose
Running a floppy soft hand...
Running a floppy soft hand guard from Moose or MSR over your metal hand guards will keep the cold air from your hands. If you really want protection, Moose has this set-up that allows you to put your hands inside for full weather protection. These allow using a lighter glove.
It is important to eliminate any cotton from your base layers. Try to use a "wicking" type material that is made of polyester or polypropylene. Dress in layers. The rule is: If you are warm before you start riding you will be too hot when you get up to speed on your bike. If you are chilly before the ride you will mostly likely be perfect once you start working. Take an extra layer of clothes with you and wear them later if need be.
If you have grip heaters and hand guards, it's possible to use summer riding gloves. If not, I would recommend winter riding gloves. Moose Racing Monarch Pass gloves have a warm, thick exterior, yet a thinner palm area allowing for more comfort. Several brands have similar products. Windstopper-type gloves are a great compromise.
Another common complaint is goggle fogging. The key is too control your body temperature. If your face is sweating, there is no chance of avoiding fogging. Some mechanical aids like a dual pane lens, the Smith Turbo model goggles with the battery powered fan inside, and the Haber Eliminator can all help. Dual-pane or anti-fog lenses may still get a bit foggy but checking out winter sports goggles is a good idea. You'll be tempted to wipe moisture out of the inside of your goggles when you stop, but there is a thin no-fog coating on the interior of the lens that will wipe away. Instead, set your goggles face-side-down on top of your radiator when parked or stuff them inside your riding jacket. They'll be dry in no time. Also, re-apply anti-fog coatings before your rides and try to keep them clean.
Spikes might make you feel...
Spikes might make you feel like you have enough traction to climb trees but you don't actually.
There you have it! A checklist of items to help you enjoy your winter snow rides. It doesn't matter if you are a full-time racer or a weekend warrior, the memories will be the same. Get your buddies, get geared up, and make the most of this winter snow!