Answer: Blue Arctic willow is hardy to zone 4 (-30 to -20) so it may be only marginally hardy in your garden. The top shouldn't die all the way to the ground, but it sounds like that's what's happening. You might plant it in a more protected place (from ice and winter winds), or plant something along side to help buffer winter storms. Otherwise, I'd just prune the dead stems out each spring to make room for new growth. Best wishes with your garden.
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