I've seen Holstein milk cows fed an all grass diet and no grain. They don't look so good. They don't milk very well, either. The owners thought they looked fine, though. If a dairy cow doesn't get adequate nutrition she will rob her own body so she can continue to make milk. If you want a milk cow that will do fairly well without grain, see if you can find a Milking Shorthorn.
Yes, I would not suggest doing 100% grassfed with a Holstein. For both beef and dairy, a small or medium size frame is best if you're doing grassfed. A large frame, especially a Holstein who also milks heavily, does not do well at all on 100% grass. She has about the same size mouth but her daily dietary requirements are far higher than that of a smaller cow, like a Jersey. A Holstein will not be able to consume enough every day to maintain her weight and produce a large amount of milk and so will get rundown and thin. Whereas a smaller cow has lower daily dietary requirements and so she has more extra calories to put towards meat or milk production. Now commercially, in a grainfed scenario, the Holstein will be more efficient at converting feed into milk than a Jersey. And a big frame steer, such as a Charolais or Simmental, will be more efficient at converting feed into beef than a small or medium size Angus steer. But if you put those same steers on 100% grass the Angus steer will do better, because he himself has lower daily requirements and so can put more excess calories towards increasing his body condition (aka beef).
This isn't hard and fast though. We've had big fat cows and the rare small skinny one. My guess is that it has to do with individual feed efficiency, but I don't know for sure. But overall, there is a definite trend that the smaller animals do better on just grass than the bigger frame animals.
I have actually looked at Milking Shorthorns. They're pricey buggers, if you can find one! But they are pretty, and I do like the dual-purpose-ness of the breed. Like you say, they do better on just grass. If I ever come across a reasonably priced good quality bull calf I'd definitely consider crossing him on my Jerseys.
My Jerseys are not skinny. In fact a cattle guy thought "Kylie," a 1st calf Jersey heifer, looked very pregnant today and she's barely 2 months along, LOL. And "Becky".... Gosh, I need to post a pic from behind her, my view when bringing her in to the barn to be milked. Her nick name could be "Butterball!" And her Jersey heifer calf looks almost like a beef calf, I'm excited to see how she'll do as a milker. Using this:
http://www.omafra.gov.on.ca/english/livestock/dairy/facts/00-109.htm , all of my Jerseys get scores between 3 and 4, which is apparently perfect (except for Becky's calf, who is definitely a 5, LOL). In the past when I was giving them grain with milking they were 4s and 4.5s. Without the grain they have dropped a small amount of body condition but the most noticable thing is lower milk production. Just to be clear, they're not kept in a small weedy eaten-down-to-the-dirt pasture and expected to graze and thrive. There are several pastures that I rotate them through. When they're finished in a pasture ("finished" = grazed down to about 2" tall) they are moved to a fresh lush pasture that has been resting since they last grazed it, about a month or so prior. And when they're finished in that pasture I move them on to the next one, and so on and so on. It works pretty well.
