Hiking is a new activity in Mongolia, but with some improvisation, its possible at places such as Gorkhi-Terelj National Park. Altough there are no warming huts and few marked trails, you'll find shelter in gers and encounter locals who are more than willing to show you the wa. There are no sherpas, but a packhorse will do nicely. Good maps, a sturdy tent and a sense of adventure will help see you through. 

Terelj  sum (district), about 55km northeast of Ulaanbaatar, is a playground for urban-weary Ulaanbaatarites. At 1600m, the area is cool and the alpine scenery magnificent, and there are great opportunities for hiking, rock climbing, swimming (in icy-cold water), rafting, horse riding and, for hard-core extreme-sports fanatics, skiing in the depths of winter. Terelj was first developed for tourism in 1964 and 30 years later it became part of Gorkhi-Terelj National Park. It's a bit crowded with ger camps these days but you can easily get away from the hustle and bustle. Be prepared for mosquitoes, especially in late summer.