In other way, does the time of vernal equinox change with altitude?
The equinoxes are defined as the points in time at which the Earth's equatorial plane intersects the center of the Sun. From an Earth-centric perspective, the Sun appears to crosses the equatorial plane from south to north at the March equinox, and from north to south at the September equinox.
Altitude, latitude, and longitude, and length of day do not come into play. In fact, days are slightly longer than are nights almost everywhere on the Earth on the dates of the equinoxes. This is a result of the Sun's angular diameter and atmospheric refraction, both of which mean we can see the Sun when the center of the Sun is a bit (0.83 degrees) below the horizon.