Sounds like my horse and my yard
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I have a 14.2 native-type at grass livery. Water is supplied automatically to the fields and they yard puts haylage out in the winter (or straw for the fatties like mine). They keep an eye on the horses, so if they are sick or obviously lame they will notice, but they don't actually go up to them and pick out their feet or anything, so I go and see him most days. If I'm away I ask a friend at the yard to take a look at him. If you really can't go every day I think you need somewhere that will do full livery as well, or friends that can look after the horse if need be. Otherwise what will you do if the horse is sick? Mine had an abscess recently and needed twice daily visits. Worth thinking what you'd do in this situation, or if your horse had to be on box rest.
I wouldn't think weekend-only riding is enough to keep a horse fit, but it will keep them ticking over.
Costs (I'm copying this from another thread I posted on), around:
125 grass livery + hay
50 insurance
50 petrol to and from yard
15 feed, carrots, supplements (e.g. garlic for flies, stuff to stop him getting green poos)
20-100 lessons (varies a lot depending how many we have)
30 barefoot trim
Varying amounts on saddle checks (he's young and growing), physio, yearly vaccinations and dentist, random vet callouts (not many of these luckily!), replacement tack/jodhpurs/riding hats/always something we need, small amounts on things like competition entry, or share of diesel money to go to the beach
So probably around 350-400 a month. 
Incidentally, he was rugged the first winter, but last winter was so mild he had a bib clip and no rug, this winter he has the same so far. Before his clip he was sweating just standing in the field. 