"Eight tiny reindeer" -- well, the number gives it away, doesn't it? Lightweights, obviously. A later tradition assigns the bow reindeer a red nose which glows (what else but the shell's bow blinker?) and attests to its efficacy during fog.
"He was chubby and plump" -- all coxswains, even those who are thin as a rail, look chubby to the rowers pulling them. This apparently contradictory piece of epistemological evidence need not distract us from our thesis.
"When out on the lawn there arose such a clatter" -- okay, so it was a bad landing.
"Dash away, dash away, dash away all" -- clearly a misprint for "hands away, hands away, hands away, all." Pause drills while docking can be tricky -- especially as it seems from the preceding line that they had just completed a power ten, in which Nick is calling the rowers by name (this might explain the clatter on the lawn referred to in the previous line).
"His cheeks were like roses; his nose like a cherry..." Cold, late season, practices will do that to a coxswain.
"His droll little mouth was drawn up like a bow" has apparently been garbled by the typesetter. "His filthy little mouth could be heard up in the bow" is a much more scholarly reading of the line.
Now that we have cleared up the textual details, what does the poem really mean? Why does it speak to us through the ages? What lessons can the rowing community draw from it? Is it merely off-season quaintness, or does it contain hidden warnings? Schopenhauer, in his monumental three-volume work "Die Gestalt des Steuermanns," describes the context as portraying a moral and ethical vacuum wherein the coxswain hero/antihero (who has no doubt been cutting weight), makes impromptu -- and unsanctioned -- landings during a night practice in order to climb down other people's chimneys and gorge (safely out of sight of the rowers) upon the cookies and milk set out on the mantlepieces by the unsuspecting residents. Hegel, more darkly, in "Die Angst und der Tillermann" speculates that the coxswain's ability -- or inability -- to steer a straight course will produce dire repercussions for the stability and permanence of society.
Whatever your interpretation, dear readers, may you enjoy a "Happy Christmas to all, and to all a good night!"