That looks awful... hope someone can help as I have babacco papaya tree too.. is paw paw the same as a babacco papaya? Meixue

Your photo doesn't indicate cold damage, but instead is evidence that yours has Ink Spot disease, which they are very prone to getting if stressed, overwatered by regular spray irrigation, or not getting enough full sun or good air exposure. Sacramento probably is borderline for best performance, unless they are in a protected microclimate that doesn't regularly freeze. I'd suggest you check the drainage, move them into full sun, cut out the diseased foliage, keep the spray irrigation off them, and avoid using any complete fertilizer with phosphorus in it. Or just treat them as annuals, as they look so healthy and full in bloom at places like Home Depot this time of year. All of my Kangaroo Paws always look their very best in winter with the full sun/perfect air circulation/perfect drainage/no overhead spray irrigation and well draining sandy soil in a garden where it stays mild and warm in winter. In my opinion, they are best along the coast, rather than inland Sacramento...

My pawpaws didn't start blooming til 4 years (and that was the grafted ones) the seedling ones haven't bloomed and this is their 5th year. There is a way to look at the twigs (after leaf fall) and see if buds are there for next spring. Look for round buds (the pointed ones will only produce leaves). ~Chills

Could you describe what is going on? Is that a black scale on one of the new trunks? I would remove the dead bits back to green tissue and seal the cuts with plastic paint with Copper-Oxychloride mixed in. But thats just a wild guess