You cannot abandon Messages Across Tamriel, as it is a Main Story quest. If you were in Coldharbour, you most likely already finished that one, and abandoned the quest that came after it. If you abandoned a quest in Coldharbour, you need to go back to where you got that quest from. If it was the first Coldharbour quest "The Hollow City", you need to look for The Groundskeeper in the Hollow City, just inside the southern entrance.

Ourorboros wrote: »

I'm not certain that you have to complete "Message Across Tamriel" to continue on with the Cold Harbor quests. I had multiple low level characters planted in Cold Harbor for writs, none of which had even completed their first zone. As Enodoc stated, get the quest from the Groundskeeper. Use the 'travel to' option for guild or group if you don't have wayshrine access to Cold Harbor.

You are correct, you don't have to complete Messages Across Tamriel to continue with the quests in Coldharbour. But OP must have already completed it anyway, as it's no longer in their Journal and it can't be abandoned.

We don't really know how far through Coldharbour OP got before abandoning a quest, so this list of Coldharbour Quests may also be useful:
http://www.uesp.net/wiki/Online:Coldharbour#Quests

Ah okay, in which case you need to go here and talk to Tzik'nith to get the next quest.