PA-24 enroute over high terrain lost partial power due to carb ice; pilot declared an emergency and diverted with the aide of ATC. Total loss of altitude was approximately three thousand feet prior to regaining full power.

Narrative

I was initially enroute VFR with flight following to ZZZ2. Midway through my trip; ceilings were lowering and I asked Center for an IFR clearance for the rest of the trip. I was in IMC soon after. I had anticipated the possible need for switching to IFR and pre-planned accordingly. BQZ was a good location to join the enroute structure because the westbound MEAs were substantially lower; and the terrain gentler; as it began to go down the Colorado western slope. Weather in the clouds at 11;000 MSL was good IMC - 0 VIS but smooth; negative turbulence; negative icing. Approximately 50 NM east of CHE; we suffered a loss of power. I had just switched tanks and so switched them back. I turned on the auxiliary fuel pump. Pitot heat was already operating - even though temperatures were well above freezing; it is my SOP to do so upon entering sustained IMC. But; although we have not yet had the airplane checked mechanically for other possibilities; I believe I delayed applying carb heat long enough that serious carburetor ice formed and that; once applied; it took a long time for the ice to clear. We never lost power completely and; although I could not hold altitude; my impression is that we descended at a normal rate ~500 FPM. I don't think we ever went much below 8;000 MSL at which point power began to return. We made an uneventful landing. In my opinion; Center did a great job and so many things about the system worked the way they are supposed to. I declared an emergency. Center gave me all the attention and help I required. ATC initially called out ZZZ1 as diversion airport (probably because it was the closest with an instrument approach). I initially turned that way; but I think we both realized at the same time that 'uphill' was not necessarily the best course of action. When ATC indicated my bearing and distance to ZZZ I elected to go there - it was closest 'downhill.' There were times that ATC and I were out of 2-way communication; and communications were relayed via other aircraft in the area. Human factors: They talk about brain lock and delayed reaction when there is an emergency. Although we check carb heat on every carbureted engine run-up; train for carb ice and teach and are taught to apply carb heat at the first sign of an unexplained loss of power; I had never experienced carb ice before - not even during instrument training in New England (summer and winter). Add to that I was at full throttle cruise flight; the prevalence of fuel injection and my flight in multiple types of aircraft (my last few flights have been part of a checkout in a fuel-injected Debonair) and I think my form of brain lock was forgetting about carb heat. Whether it was just a minute or so or more; it's clear that it was long enough for what should have been a minor inconvenience to become a serious problem. On the other hand; there are parts of this that went well; even in terms of me (again; ATC was fantastic and there's no doubt that dumb luck played a big part). My general instrument training took over and loss of control (even though I have no autopilot) was never an issue. I had selected my entry into the system at a good location where terrain was becoming both lower and leveler. I recognized that the terrain toward ZZZ was 'downhill' - in fact I don't believe that I even received a terrain warning from my GPS - indicating that I was always at least 1;000' above the terrain. As a pilot; I know I will never forget the lesson this has taught me. As a CFI; my experience will be part of what I teach. It wouldn't have taken but one more bad thing to have changed the result of the experience.