Yes, especially if it means your living room faces North too.
It's lovely both to sit in the sun on a summer evening and look out on a bright sunny, if cold garden in winter. winter Sun saves oil too. Our old front room was always cold.
We actually have the opposite problem here, both front and back gardens face South (back garden is raised up, so only the drive is in the shade of the house). Except for tiny corners under hedges, everything gets baked.
Lavender and poppies are happy, fuchsia and some bedding plants really aren't convinced.