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In this weather, yes. It gets much thicker when it's cold. I always stir the Zinsser products a decent amount before applying. I had forgotten about the temperature issues as I avoid exterior work in the winter. Sorry about that.
You could try warming the pot in water or next to a radiator. There's a neat paint warming kettle solution that's popular in some of the colder european climates.
Tried the Cover Stain. It does block the tannin stains nicely, however it is horrible to apply. It has been a while since I used an oil based paint but I think this is particularly challenging.