I certainly wouldn't put water barrels in an exposed, unheated greenhouse in winter. And it might not be a great idea to pile a lot of extra weight on a deck - don't know what the support structure is.
One thing you can do cheaply to add a couple of weeks to your growing season is make a mini-greenhouse inside the greenhouse. Put a sheet of foam insulation in the bottom of the tent, install a light fixture and a heating pad. For most seeds to germinate, you do need the heating pad, at least for the night. If you're lucky, sun will give you enough heat in the daytime. Keep the seedlings well watered.
It doesn't need to be this big - it's my nursery. The hatchery is three bookshelves in the dining room.
If you organize the space well, you can add up to a month to the fall, as well. Keep some plants in portable containers on or near the deck and bring them into the greenhouse before September frost. You can rig up a temporary plastic tent for them, too.