I would see how she settles in first, just on grass & hay. Especially if you say she needs to lose some weight. If you are only going to do light work with her, then that should really be enough.
There is no point feeding her grain if it will only give her extra energy, or add to her weight.
You can always reward her with a small tasty treat after you ride her. Nothing too fancy, even just a mix of chaff & molassess, or carrots.
If you think she is losing too much weight, then consider feeding her more ;o)