feces on boxes after a several cold days

I see a 1-2 bee entrance, yet two (deep/medium?) boxes...?? More info needed please... The droppings don't look healthy to me, but more info needed.

I hived 2 new packages about one month ago. They both have two deeps, with a 3/8" hole in each box for ventilation. Both hives appear to be doing well on inspections. Each have 6 or 7 frames of brood and are starting to draw out foundation on upper box that was added a couple of days ago.

Try checking your sugar syrup to see if it has fermented. Heavily fermented sugar syrup can and does cause symptoms like you posted. If your sugar syrup has fermented, dump it out in a place where the bees cannot get to it and mix up a new batch of sugar syrup treated with Honey Bee Healthy or Mann Lake Pro Bee Health. (this will prevent fermenting). If your sugar syrup is not fermented and in good shape, you may have some Nosema issues to deal with which would require mixing up a batch of sugar syrup treated with Fumagilan-B.

It could also be that your bees have found something tempting for them to eat that is causing this such as some rotted fruit or garbage somewhere nearby.

I have the same kind of thing on my hive, thought maybe it was from the cold or from the protein patty they where eating in the hive. I have no sugar water as it was a hive all drawn out with ample stores when i put them in place 3 weeks ago.