I seek a book in the offing: Jogging in Mongolia, about a young man from Hong Kong who trades his job as a financial analyst to move to Mongolia to teach goat herders how to use an Excel spreadsheet.
But even if this isnt your fate, theres no doubt itll be cold. But too cold to do some exercise? Well, yes and know. Lets say its -20 Celsius. Thats -4 Fahrenheit. Which is pretty coldespecially if its windy. But you could go and do a run or a little skiing. I wouldnt wander too far, or commit to anything more than 30 minutes at a time until you see how it goes. But why not?
The big question is: What to wear? Lets say you wanted to go for a short run. Id probably wear something like:
A synthetic T-shirt such as REIs Mesh RTS Crew ($22) (Im not sure what you can find in Hong Konggo to a sporting good store and find a light T-shirt made from polyester).
Same thing for the legs.
A heavier layer for torso and arms. My first choice would be a midweight wool long-sleeve T like Patagonias Mens Wool 2 Crew ($70). There are other brands, of course. The key is to find a store that carries high-end Merino wool clothing.
A shell for legs and upper body. Asics Storm Shelter Jacket ($100) would do nicely. Its waterproof, if you need it, and also wind-proof. Nikes Dri-Fit Running Pant ($60) would be a good choice over the legs.
Gloves and a warm hat.
That should get you off to a good start. You can build on this basic kitanother layer here or thereto get where you need. And beware of frostbite! Especially on your face. You might need to get a face mask or a neck gaiter of some sort to ensure your cheeks or nose dont freeze. And remember that cold weather really saps the body of moisture, so be sure to stay hydrated.
For cross-country skiing, a warmer mid layerThe North Faces Pumori Jacket ($99) comes to mind)would be useful.
In any event, have fun! Send a picture.