[William Cloud Hicklin]

It appears from "The Disaster of the Gladden Fields" that the only way to avoid the treacherous marshlands was to skirt the borders of Mirkwood, not far from Dol Guldur: bad idea.

The principal advantage to the Dimrill Stair was that it debouched almost directly into Lothlorien, and avoided a lengthy march through the narrow lands between Mirkwood and the Mountains. From Gandalf's perspective it made perfect sense to minimize the Company's exposure in enemy-infested territory for as long as possible; and, of course, if you're going to cross mountains in January farther south as a rule is safer. Elrond's scouts had used both northern passes in November/December, true: but they were Elves, and probably no more discommoded by snow and cold than Legolas was.

EDIT: replaced "Rivendell" with "Lorien", which was what I meant.