We report the observation of hole cyclotron resonance (CR) in InMnAs/(Al,Ga)Sb heterostructures in a wide temperature range covering both the paramagnetic and ferromagnetic phases. We observed two pronounced resonances that exhibit drastic changes in position, linewidth, and intensity at a temperature higher than the Curie temperature, indicating possible local magnetic ordering or clustering. We attribute the two resonances to the fundamental CR transitions expected for delocalized valence-band holes in the quantum limt. Using an 8-band {bf k$cdot$p} model, which incorporates ferromagnetism within a mean-field approximation, we show that the temperature-dependent CR peak shift is a direct measure of the carrier-Mn exchange interaction. Significant line narrowing was observed at low temperatures, which we interpret as the suppression of localized spin fluctuations.