Having a base layer of insulation all across your body will greatly aid in keeping you warm and comfortable while out viewing Aurora. You can add this to clothing you already have for additional warmth.
Socks: I suggest a high quality wool sock in addition to your warmest boot.
Snow Pants: This one here can often be found for $15-20, I personalty own a pair and the insulation is light to moderate. For a better insulated and more expensive type look at Columbia's snow pants, they are a bit warmer.
Long Underwear: For the depths of winter wear men's or women's long underwear under your snow pants for extra warmth. For late August and September you could get away with just long underwear and jeans for most nights.
Long Sleeve Wicking Shirt: You will want a quick drying long sleeve shirt for a base layer like this Hanes men's or woman's shirt.
Long Sleeve Warm Shirt: After your base layer when it is very cold you want to wear a shirt with insulation. My favorite is a men's or woman's Woolrich wool shirt, they are very warm. They aren't as warm as wool but a men's flannel or woman's flannel shirt are warm and a lot cheaper.
Insulated Mid-Layer: I personally prefer Columbia's insulated jackets for men. When it is really cold you will need a winter coat outside of this.
Gloves: My strategy for photography is to wear light gloves like this for men or women that I can operate the camera with and put my hands in warm coat pockets the rest of the time.
Hat: You should bring your warmest hat, if you don't have a winter hat and want a relatively inexpensive one look into the trapper hats. No matter what hat you bring getting a good Turtle Fur Fleece will make it that much warmer, it is highly recommended.
Hand warmers are nice to have too.