Not being an archaeologist, I can look to two other reasons. The fourteenth century also saw the Aztec empire expanding, and that would have resulted in waves of migration radiating away. And if archaeologists were wrong about the date, I'd also consider the Spanish wipeout of the Aztecs starting even larger migrations. The latter would be especially significant, because it would include horses.
 

A typical family group: two adults and a child in the middle. Most archaelogists refer to it as a headhunter scenario.

The Fremonts lived in a remarkably safe area. To the east are the Rocky Mountains; to the north, the Unita Mountains; to the west the Wasatch Range (or plateau or mountains); to the south, if not named, also mountain passes. Not only is the land desert, but they were farmers. People are generally driven to such places and survive in them because no one else wants to live there.
 

One robust petroglyph nearly superimposed on a fainter one. It is impossible to predict the rationale, because weathering has a very strong effect.

Horses would have had quite an impact on the area, making the inacessible open. Or such are my thoughts. I suppose though that it is too easy to speculate on the life and times of a vanished people, one without a written record. All that is left of the Fremont are artwork and implements. I don't know about the implements, but their artwork is stunning - free and open - having a dynamism typically lost through "education."
 

A very detailed person, along with a kid to the left, and what looks to be a glass of champagne to the right. Faintly drawn, though, is what appears to be a face over the "glass." A Fremont teenager?