Arne, I did that route as my first pre-Whitney acclimation hike last August, and it's not too bad. It's only about 1000 feet of elevation gain, and there are no really steep areas to negotiate, but no matter how you slice it you're still hiking from a 10K' trailhead up to 11K'. If you're acclimated, it shouldn't be tough at all.
I had not acclimated before heading for the trailhead for that first hike, so that slowed me down some. Flew from Atlanta to Vegas the day before, then drove from Vegas to Lone Pine. Checked into my hotel about 8 pm and was at Horseshoe Meadow at 7 am the next morning. Not the best way to start acclimating to 10K', but I was pressed for time. I'm sure if I had spent the night before at 8K', it would have been a lot easier. I had a mild headache most of the hike, but nothing more. I went back the next day and hiked the Cottonwood Pass trail - a tougher hike - and pretty much breezed through it.
If you're not familiar with the trails out of Horseshoe Meadow, be warned - the first mile or two is in ridiculously soft sand and takes a helluva lot more energy for each step than most places you might hike. I thought I was at a 2-mile high beach. Once you start climbing out of the meadow, though, the trails firm up a bit.
