The cold weather I'm experiencing doesn't appear to be isolated to my region; it seems nearly the entire northern hemisphere is having an unusually cold winter. Here are some ideas that are working for me in coping with the chilly conditions:
Bundling Up: The vast majority of people I hear complaining about the weather are people who are wearing far fewer clothes than I am. If you're in a mini-skirt with only one pair of tights on, I don't want to hear about how cold you are.
I'm an advocate of layers, preferably in animal-derived fabrics like wool, cashmere, leather and silk. Cotton just isn't as good an insulator. I like "performance" fabrics too (man-made fabrics that are engineered with special insulating and/or wicking properties), but find that these tend to be pricey and don't integrate into my everyday wardrobe as easily. If you have ethical concerns about animal fabrics, these are an especially good option.
My general formula for layers on the top are shirt + sweater + coat and then double at least one of the components. For instance, today I'm wearing two shirts, one sweater, a blazer and a coat. Bonus: Layers are in style this season!
In cold weather, I always wear at least two pairs of pants (silk thermal pants under regular pants being my favorite combination) but have had success wearing up to four pairs of pants. (Unlike most people whose hands or feet normally get cold, I'm a freak and it's my legs that are always cold.)
Also, your mom was right; wear a hat. Top the whole look off with a scarf and gloves.
Thoughts on gloves: Commit to one style of gloves for the rest of your life. That way when (not if) you lose a glove, you can save the one you still have and match it when subsequent pairs of gloves lose their mate. I prefer cashmere lined black leather gloves.
Dry Skin, Nails, and Hair: Where I live, cold weather means very low humidity which causes my skin to become very dry. I've even had my skin crack open and bleed from dryness.
Showering less frequently is one way to reduce skin's dry, itchy feeling. If you can't go a day without bathing, try to take shorter, cooler showers.
Exfoliate! If exfoliation had a fan club, I'd be its president. I exfoliate year 'round because I think it keeps my skin feeling soft, makes me look younger and prevents wrinkles, but in winter exfoliation has the added benefit of getting rid of dry, flaky, itchy skin. Both chemical (glycolic acid, alpha hydroxy acid, etc.) and manual (scrubs, textured washcloths, etc.) exfoliation are effective in getting rid of itchy skin.
If you haven't already, try a milder soap. I love deodorant body soap in the summer when I'm always sweaty, sticky and gross, but in the winter, I want soothing, moisturizing soap. Savon de Marseilles is one great option.
You're probably already moisturizing, but are you moisturizing your nails too? I find that my normally strong nails are much more likely to break in winter. Keeping them lubricated helps them to maintain their strength and flexibility. One inexpensive, but controversial, way to do this is slathering your hands and nails with petroleum jelly before going to bed. It was good enough for my grandmothers and it works better than anything else I've tried so I'm going to stick with it even though some people believe it poses certain health risks. (WebMD also recommends petroleum jelly.)
Prevent hair damage in winter months by never going outside with wet hair. It is better to blow dry than go outside in cold weather with wet hair. If you don't want to blow dry, wash your hair at night so you don't have to go out with a wet head.