I am guessing that when you say "we've" that you are talking about more than just yourself. In other words, you have more than one person in the tent. A hammock sleeps one. It does not sleep two comfortably. Yes, there are hammocks that do sleep 2 comfortably, but they are just 2 hammocks attached to each other. You save weight by using the same tarp, other than that, it is the same as having two different hammocks. If your "other" is a dog, then your dog needs to be able to sleep under your hammock. This might be a problem in the cold. My last dog (see my avatar) would sleep in the snow, despite me getting her a pad.

So, like others have said, yes it is possible to make a warm hammock. However, you need to take into consideration how many you plan to accommodate.