I am no expert on this, and I hope others will chime into this topic. My experience last year (mid-December, SW WA) was in the middle of waves of rain, which lasted several days. We never saw elk when it was really coming down, and we were out from dawn to dusk. Finally, on the third day (last day of the season), the weather broke. We found a herd of 20+ cows & calves (no bulls) on a ridge road, sunning themselves midday. But that was the only group of animals we saw the entire long weekend.
Given that late muzzleloader and late archery mostly overlap in western Washington, and given that rain is the predominant weather pattern, I would say: "Look for open areas (grassy knobs, recent clearcuts, <3 year old trees), and wait for very light rain or dry opportunities." In my experience, very windy and/or very rainy days are not productive for late season elk.
Anybody know better than this??