In my experience, in a heavy downpour rain, the muleys tuck tail & take cover in heavy, thick brush, timber.
A choice area that is out of or protected from the wind.
But when that storm breaks,
that is the time to be hunting.
This is a last day of the season, young 4x3 WA State high country mule deer buck, taken after a 2-day storm broke. I too had taken cover for 3.5 hours underneath some thick pines, keeping relatively dry with my raingear on. Storm broke, winds & thermal shifted at 4:30pm, fog came in & out....and the deer were everywhere below me in the basin. Feeling damp and cold, I had only 30 minutes of hunting light left. With over 50 deer below me, I had to act fast to fill my deer tag within the last hour of the season.
A 225-yard downhill shot and the buck tumbled head over hoofs, down into the bedding pines. A small fir tree stopped its progress, thankfully as another 20 yards was a near 60' vertical drop off a cliff.
I didn't get back to spike camp until 11pm, after processing, deboning and hanging the deer meat in a tall pine. Took me the next 1.5 days to pack out the meat solo.
Image of my last trip pack out. Left the Browning Belgium scoped 300 Win-Mag locked up at base camp. Brought along the old family Winchester, 32 Win-Spl as predator protection.
