I wouldn't bed Shetlands on anything they can eat, because you then lose control of a restricted diet.
We feed hay all year, to try to counteract grass sickness which is common here, but grazing is VERY restricted during the summer. At the moment they are strip grazing a paddock during the day, getting two wee chaff feeds and 6kg of hay between them. In winter, I feed hay, not the very best, but will give them a leaf or two of straw every day is they are hanging around the gate. Oat straw is best, but I have barley straw so use that.
I work on ponies needing 1% of their bodyweight in forage to maintain gut function and 2% to maintain weight, so I feed somewhere between that, depending on how fat they are and how much grass there is.
The total weight of our three is about 1150kg, so last winter in the snow, I was feeding 18kg of hay a day in three feeds plus their buckets.