There was a program on Snowball Earth last night and they said that the presence of glaciers at the equator meant that the whole Earth was covered in snow and ice. This sounds a pretty reasonable conclusion.
But how do they know that the equatorial glaciers weren’t at high altitudes? Only to sink later, like Tibet. And is there really enough water around to freeze the entire Earth?
The geological evidence for Snowball Earth is controversial and far from be accepted by all; see the Wiki article for examples.
One kind of evidence that would demonstrate glaciation at sea level rather than at high elevations is dropstones in marine sediments. These are boulders and other debris carried to sea in icebergs which are dropped in deep water when the berg melts.
To get large numbers of dropstones, the source would be expected to be fairly close to the Equator. In the North Atlantic today, icebergs rarely get south of 40 degrees north, and the southernmost record is 30 north. By the time bergs get that far south they are so small they aren’t carrying much.
Also, the Precambrian didn’t really have mountains in the Phanerozoic sense. Without any life on land, erosion was incredibly quick and mountains were eroded almost as quickly as they uplifted. Land would have been essentially a flat featureless plain, perhaps with some regional high areas, but certainly no tall steep mountains in the sense we think of them.