General aviation pilot reported temporary loss of aircraft control while flying through windshear and turbulence over mountainous terrain.

Narrative

I was flying Aircraft X from ZZZ to Gunnison (GUC). I departed at XA:10 and landed at Gunnison at XD:43. I filed an IFR flight plan. The conditions on the entire flight were VMC. My approved flight plan was ZZZZZX; ZZZ [VOR]; ZZZ1; GOSIP; BLOKE; GUC. Shortly after my departer I was cleared direct ZZZ [VOR] and followed my flight plan. I had filed for 12;000 feet knowing that after GOSIP; I would be cleared for 14;000 for the IFR corridor. After departing GOSIP to BLOKE; over La Veta pass; I experienced strong headwinds of approximately 30+ kts. Over the pass; I experienced wind sheer and turbulence that hindered my ability to maintain an altitude of 14;000. My altitude fluctuated 500 to 1;000 feet from my assigned altitude. I was on Autopilot and 2 or 3 times; the Autopilot struggled to maintain 14;000 feet. The Autopilot attempted to maintain altitude but was struggling to maintain a safe airspeed to maintain the altitude. At a couple of points; the airspeed got dangerously low to stall speed. My Autopilot indicated an airspeed warning as did my flight instruments; and at one point an airspeed warning horn activated in my headset. At these points; I disengaged the Autopilot so I could take control over the airspeed. In order to regain controllable airspeed; I was required to tip the nose down. These efforts to maintain a safe airspeed and due to the wind shear and turbulence resulted in the fluctuations in altitude. Due to the turbulence; windshear; and correction for airspeed; my altitude dropped at the lowest point to 12;400 feet although the IFR route required a minimum altitude of 14;000 fee. After passing through La Veta pass; I was able to climb back to 14;000 and proceeded to GUC with no other altitude deviations. I was in VMC the entire time; I had the terrain in sight; and therefore there were no terrain hazards. While confronted with certain situations; a pilot is first to aviate and then communicate; I probably should have communicated with ATC earlier in this process of recovering from the slow speed and altitude loss to advise ATC of what was happening. Ultimately; when ATC noticed the altitude loss; they contacted me and I explained the situation.