Gravity waves (GWs) play an important role in the dynamics and energetics of the mesosphere. Geomagnetic activity is a known source of GWs in the upper atmosphere. However, how deep the effects of geomagnetic activity induced GWs penetrate into the mesosphere remains an open question. We use temperature measurements from the SABER/TIMED instrument between 2002 - 2018 to study the variations of mesospheric GW activity following intense geomagnetic disturbances identified by AE and Dst indices. By considering several case studies, we show for the first time that the GWs forced by geomagnetic activity can propagate down to about 80 km in the high latitude mesosphere. Only regions above 55° latitudes show a clear response. The fraction of cases in which there is an unambiguous enhancement in GW activity following the onset of geomagnetic disturbance is smaller during summer than other seasons. Only about half of the events show an unambiguous increase in GW activity during non-summer periods and about one quarter of the events in summer show an enhancement in GWs. In addition, we also find that the high latitude mesopause is seen to descend in altitude following onset of geomagnetic activity in the non-summer high latitude region.