"Did women wear corsets on the trail?"

In all probability and given the practical nature of the women making the journey, they probably would not have been "laced to extremes" while traveling. (Watson, Travails, p.32) But once these women settled in and created a social structure, entertained, attended balls and parties, the corset would be a necessity.

"Why wear corsets?"

The corsets of the 1840s and 1850s provided a woman with support and protection much as the bra does today. The corsets of the 1860s -- think Scarlet O'Hara -- aimed to create a more defined structure, support for the skirt over the hips and a smaller waist. This was possible with tight lacing and the use of whale bones for support.