For the most part they do not openly partner with one side, though they do seem to favor sides indirectly. Sometimes the sides themselves favor guilds in small ways.
Take for example the Dark Brotherhood - the end objective is to the kill the Titus Mede the II, the leader of the Empire. It clearly favors the Stormcloaks, though the Dark Brotherhood in not allied with them.
While for the Thieves Guild having the Empire be rulers of the Rift is most advantageous, placing Maven as Jarl therefore granting more influence over the region for the Guild.
These storyline theories have no influence over the players gameplay, but it is still fun to speculate which guild favors which side in a storied and roleplaying manner.
What is your opinion? Which side do you think the Companions and College favor indirectly or otherwise? Do you have a counter proposal regarding the Thieves Guild or Dark Brotherhood? Knowing the outcomes of the guilds, does this affect the way you roleplay the game?
Good answers. Also the College, if forced to side, would probably side with the Empire due to the fear of magic from the nords. The Companions seem to have a few Stormcloak sympathizer associates ( Vignar Grey-Mane, Eorlund Gray-Mane), and no Empire sympathizer associates, which reinforces unspoken support to the Stormcloaks.