He's going to loose weight like crazy and not going to fatten up at all on just or primarily grass-hay, as a Holstein and a young, growing calf, and that's even if the hay is as good quality as grass hay can get. As a Holstein and a 300 lb calf he'll need around 14% protein and even a bit of energy. You'll need to feed him grain quite a bit in addition to the hay.
Figure in 2.5% of his body weight in dry matter ration per day. That's how much a bovine of any weight will eat per day. In as-fed form, you need to factor in the moisture content of the hay. Assuming that the grass hay has around 20% moisture (or 80% dry matter), I can try to do the math for you then:
2.5% x 300 lbs = 7.5 lb per day
7.5 lb per day / 0.8 as-is dry matter content of hay = 9.4 lb per day
That's all assuming that the hay is high quality; cattle tend to eat more if the forage his higher quality than if they were to eat lower quality feed. You will also have to expect a 30% increase in intake in colder conditions, which could boost feed intake to around 31 lbs or more per day. If he were loosing weight and you were trying to get him to gain weight again, you may also see a boost in rate of intake. So, to avoid this, supplement the calf with grain to keep him in good shape and keep him from losing weight over winter.
Also, I wouldn't compare Mike's Highlands (very tough, easy-doing, easy-keeping (like they can do just fine on just hay over winter) beef cattle that require minimal management) to your Holstein (dairy, hard-doing, require higher-energy rations, and poor-ding as far as minimal management for a beef animal is concerned) because you'll be comparing apples to oranges.