Ynot, there is an ad for aero garden on your page.
They are cute, but not for really serious gardeners.
They are nice to keep a few herbs.
There is also another type of hydroponic gardening which is off the ground but done outside.
The pots are on poles.
I think you would be getting into a lot of expense to go hydroponic. You have a lot of electrical equipment, constant running water, and must add special costly fertilizer all the time.
Perhaps it would be less expensive to make the gate more secure or purchase something to keep the deer and other rascals away. I know there are some sonic things and some smelly things...I have seen stuff advertised.
Or...you can entice the deer back and shoot 'em. Get your greens back recycled as venison!