I don't believe LDS Cosmology addresses St. Thomas specifically, but your quote suggests that the LDS reject his argument: "Mormons deny ex nihilo creation." In other words, the LDS believe that everything that exists has always existed (in some form)--it needn't have a first cause. Now let me address St. Thomas Aquinas' argument:
St. Thomas used an argument of a causality which I will illustrate: suppose a chain is dangling in the air. The bottom link hangs because it is supported by the link above it, which, in turn is supported by the link above it--all the way up the chain. St. Thomas would argue that there must be a first cause (e.g. a hook on the ceiling) because an infinite regress of links would mean that the whole chain was held up by nothing, an impossibility. This is the weakness in this argument.
A dangling chain that stretches infinity into the sky is, quite literally, held up by itself. Ignoring cosmic factors like earth rotation and orbit, if the chain is to fall, the gravity of the earth must cause it to accelerate toward the ground. Because the chain stretches away from the earth an infinite distance, its rate of acceleration would be infinitesimally slow (acceleration due to gravity decreases with altitude). Hence the chain would never reach the ground.
In other words, an infinite chain of causes without a first cause is not theoretically impossible.