The soldiers retained their infantry arms, uniforms, and gear, and when they fought, they usually dismounted and fought as traditional infantry skirmishers. The "mounted" aspect was just to get them around faster.
After being mounted, the Orphan Brigade acted mostly as scouts, operating on the flanks of Sherman's forces in his March to the Sea. Most of the actions that they fought in as mounted infantry were small skirmishes, with only a couple "pitched battles."
Confusion can arise because when the War Dept. clerks were compiling the soldiers' military service records, they marked ALL of these records for the Orphan Brigade soldiers as "Mtd. Inf.," even though that designation did not apply until Sept. 1864. So, if the soldier you are researching left the 5th Ky. Inf. before Sept. 1864 (died, disabled, POW, transferred, whatever), he did not serve in the mounted infantry, although his service record will be marked that way.
Geoff Walden