The gate you're referring to is immediately after the kilns, and it was closed when I climbed Wildrose the end of December. Assuming you can drive as far as the kilns, that will add a couple of miles and approx 1K'+ to your hike.
Have done a couple of hikes in the Panamints in the last few days. Expect snow, depending upon the exposure, somewhere around 7K'.
Right now the weather looks stable for the next several days.