Hi,
you are right, traveling in Mongolia, you will find many possibilities to stay. Along the main tracks, there are "truck stops", and in the more remote regions you will be readily invited by locals. You will be offered food, and they will cook for you.

Although this sounds really great, you should be aware that the Mongolian food is very different from what we are used to, involving a lot of meat and milk products, few carbohydrates, and they drink fermented horse milk as their favorite drink.
It takes a while to get used to (we both were sick a couple of times during our trip), and from my own experience I found too little carbohydrate in their meals to allow my body to recover from a hard day cycling.
If you are invited, the family will be very grateful if you took their pictures with a poaroid camera. We actually carried one only for these occasions, and it was worth the extra weight.