I'm not sure what your question is - is it can you keep horses with no one there to supervise and you only visiting once a week?
I would say that it is very risky. It could be done with the right horses and the right set up - very good fence, turnout with access to shelter, good grass, unlimited access to water.
We frequently leave our place for up to a week at a time and no one has to do anything with the horses BUT there is someone observing them and able to intervene if something goes wrong, that's a key difference. And they are not feed grain, and do fine with either free choice grazing or free choice hay.
Feeding any kind of grain in this set up, even with automatic feeders, puts a whole other level of risk to it. Over or under feeding, one horse getting all the food, one horse going off his feed and no one noticing, etc.
The real risk with this set up is a horse getting ill or injured when no one's there to notice or fence getting damaged/horses getting out with no one to notice.
If you have a close neighbor or someone who will run an eyeball over the place and horses on a regular basis, I would say it's doable. Otherwise, I'd be very concerned about what all could go wrong in your absence.