We will go anywhere anytime in Europe to fulfill the fantasy of an old old inn with fireplace in a snow setting with possibiltiy of horse drawn sleds, the less "touristy" the better, and middle price range. We live in California and miss snow but don't ski or do sports.

I was at La Mainaz (http://www.la-mainaz.com) in March 2007 with snow everywhere. It was fantastic. You can forget about horse drawn sleds though, because those are only in the ultra touristy resorts like Zermatt.

No offense, but if such a place exists, do you have any idea how they'd keep the thousands of tourists away who would love to find such a place?

Have a look at northern Sweden/Lapland. You are more or less guaranteed snow there - the sled maybe reindeer drawn rather than horse drawn, but that's a minor detail.

Eastern carpathian mountains (Ukraine, Romania)

I posted a reply on your "old stone or wood inn" thread, but I'll add more here. In Kandersteg, Switzerland, there is a 250-year old inn that has been very gently updated, and still retains the "old" look---Landgasthof Reudihaus. I haven't stayed there, but I have been inside to look around--it's lovely (if you like dark wood).

http://www.doldenhorn-ruedihus.ch/

Here's a description from Karen Brown's guide:

http://tinyurl.com/2hv85a

For sleigh rides, look on www.kandersteg.ch
and
www.oeschinensee.ch

They offer coach rides in the summer from the top of the chairlift to the hotel at the lake; I don't know if they change to a sleigh in the sinter. (The hotel at the lake is open for meals only during the winter.)

Morgex Courmayeur area on the Italian side of Monte Blanc has a lot of places that might fit.
http://www.hoteldolonne.com/homeeng.htm
Beautiful area.

http://www.waldhaus-sils.ch/

Humanone, If you change your mind about going to Europe and go to Michigan's Upper Peninsula instead, I bet you can find it. The sleds, of course, will be somewhat touristy but you can be assured of a ton of snow and easily find old inns with fireplaces! There.... You saved some serious money.