パドル -What does it actually mean?

Question

I believe, many of you have already seen this meme.

In short, in a PlayStation game Fate/Extra an anime girl is singing Jingle bells-like song in Japanese:

走{はし}れ艝{そり}よ
風{かぜ}のように
月{ずき}見晴{みは}らを
パドルパドル！

Source: Full original scene recording on YouTube

I just started to wonder, what does it exactly mean?

Jisho considers it as a paddle

A paddle is a tool used for pushing against liquids, either as a form of propulsion in a boat or as an implement for mixing.

Among other meanings, Japanese Wikipedia also considers it as a paddle or something similar. At the Trivia section (here), I have found that it can also mean some kind of punishment enforced in navy or former schools.

Is it a kind of onomatopoeia with a meaning similar to Jingle bells? Or maybe it stands for some kind of whip given to bad behaved children or something similar?

Answer 1

This song is basically a parody of a Japanese translated version of Jingle Bells; the original line is 雪の中を軽くはやく, not 月海原をパドルパドル. Looks like even Japanese Fate fans do not understand what this パドル means (see this and this for example), but most people seem to guess it is related to English "paddle" (either as a simple noun パドル or a verb form パドる). A few people have noticed this English word is sometimes associated with a kind of punishment, but almost no Japanese people know such a fact, so I doubt this is relevant.

Answer 2

Paddle paddle. Probably referring to hagoita used in hanetsuki (Japanese badminton), a traditional Japanese New Year's game often played by girls.

And/or staying with the movement theme as in wading through Tsukimihara U.