Asparagus not going dormant?

I'm new to growing asparagus and this is only my second winter of it. Outside in the serious below-freezing weather, I'm sure it's dormant and not a problem, but in my greenhouse, which is only barely below freezing at night, I've had trouble convincing it to stay dormant. Last year it was new from seed the preceding summer, and produced a few spears now and again in December, January and February. This year, the asparagus in the greenhouse is those same plants, which are now 3 nice big plants that I didn't harvest, but a few days ago produced 3 fat gorgeous spears. And again, one of the newly seeded this year plants put up a clump of spears, one nice and big and like 10 skinny ones.

I cut them down when some were going golden in November, and mulched with a few inches of leaves.

Should I let them grow up now in December, knowing that the greenhouse will only get colder in Jan? Or should I snap them off? How can I convince it to stay dormant? Is there a lullaby that works?

I also grow asparagus (from seed) in a non-traditional area for asparagus, in a container. Mine don't go dormant, and don't even turn yellow (the line between summer and winter here is getting harder and harder to discern every year). I cut them when they are starting to show buds, because I want them to get a bit stronger (they are maybe 4 years old, I divided them about 6 months ago). I get shoots at the weirdest times and try to just roll with it.

Asparagus goes dormant at weird times here, usually in the Summer when it gets hot and dry, and sometimes in the Winter if it gets cold and/or dry enough.  I think cutting it hard back once a year can give it a sufficient rest period if it doesn't seem to want to go dormant at all.  Feed it extra during growing times just in case.

I'm glad you posted this, because I just found one of mine trying to come up. I'd was worried that it would run out of energy and struggle next spring. Sounds like it should be okay, though.

Himalayan weather is not my forte but would like to climb a few of those mountains!

Grew asparagus for many years in TX. Any that were still standing on Jan 1st got chopped down. Here in TN it is colder with earlier winter temps so I cut the last few down towards the end of November. Never had a problem with that technique. They need a dormant season. At the same time ... I think if I saw newly emerging large sprouts like in your pic I'd wait a while longer before chopping. I wait until most of the plants are already brown.

Those thin baby plants in centex I would just let grow.