Here are the dates and locations where the companies were mustered into service.
Co. A—January 1, 1863, at Dover.
Co. B—January 31, 1863, at Clarksville.
Co. C—February 9, 1863, in Searcy County.
Co. D—February 14, 1863, at Dardanelle.
Co. E—February 21, 1863, in Johnson County.
Co. G—August 31, 1863, at Kingston.
Co. H—April 25, 1863, at Dover.
Co. K—June 9, 1863, at Clarksville.
Co. L—October 1, 1863, at Mount Ida.
Co. M—September 15, 1863, in Johnson County.
Widow's pension applications are a real crapshoot. Some of them contain good military information, but many do not. In many cases, the affidavits of old comrades of the husband are more informative than the widow's statements. In any case, I think it would be worthwhile to get a copy of the application. Who knows, you may get just what you're looking for. If nothing else, there should be some useful genealogical information in the application.
If you order a copy, how about posting a summary for others who may be researching Hill's Cavalry? Every little bit helps.