I found the exact reverse with the jog. One day I went into the mountains with a cuff on my wrist and took a bunch of measurements. I wasn't jogging but I had something like 25 pounds on my back and was definitely pushing myself.

There was a huge effect from perceived temperature--while I didn't do the cold plunge I got some quite high readings when I was on the chilly side. Yet I could get low-normal readings with my heart rate above 130 which is the highest I could go at that elevation. Obviously I couldn't actually take a reading while moving but I could have it on my wrist, stop and immediately press the button. The pattern I observed was activity raises temperature which lowers blood pressure.