Nylon isn't so bad actually. My favourite cold weather mittens are made of polycotton (65/35 I believe), and with them I use a pair of finger gloves for walking/skiing, and a pair of wool mittens for resting or when it's really cold. They're made by hestra (
www.hestrausa.com for the US) but the exact modell isn't available there, the closest resembling mine is the pullover mitt, under 'alpine race'. They have some leather mittens to, though I couldn't find any uninsulated ones. ( I have a pair of sealskin mittens that I rate vary high, unfortunatly they are almost always too warm). The pullover mittens I have have lasted over 4 years, and they have seen a lot of use. The liners you get aren't so good, I prefer knitted mittens, which are thicker and more hard wearing than the wool pile you get.
For leather mittens there is a lot of surplus stuff available here, sometimes you can find swedish (or, norweigan, swiss or other countries with a lot of snow) surplus in the states too, cheap as chips and tough as nails (though they are white usually). Look at
This site for example. Although the swedish ones there isn't the best, there are some which are made in all leather, and are completely white. Scour the evilbay, and I'm sure you'll find something which suits you.
Good luck!