General aviation pilot reported temporary loss of aircraft control after entering IMC.

Narrative

I was flying VFR from ZZZ to ZZZ1. At XA:53pm; I noticed haze or cloud. I couldn't tell; so I called for a popup IFR. At XA:54; I entered the cloud; and within a minute my IAS dropped from 150 to 50 within seconds (pitot tube frozen most likely). This caused my G500 to activate envelope protection which pitched the nose down 30 degrees. I lost 3000 feet in less than a minute. I could not fight the envelope protection using elevator; so I had to cut the throttle to idle to slow down and was then able to recover attitude. IAS returned to normal; perhaps due to unclogged pitot? I made a call to ATC saying that I had an equipment failure that seemed to be under control which caused my loss of altitude. They acknowledged and asked if I needed assistance. I declined. I wonder if I entered an area with convective sigmet. I was not told this by ATC. I could see the ground as I was pitched down; so I was not in hard IMC conditions. But; the weather certainly seemed to have played a factor. I did not receive a pitot heat warning on my G500 Txi. I plan to have that checked in the settings.