Is it permissible to go on a row boat, canoe, or paddle boat on Shabbos? 

There is a specific prohibition against using any type of boat or other flotation device on Shabbos and/or Yom Tov, even on a private lake etc. (though it may be permissible in certain specific types of swimming pools).

 

Sources:

.גמ’ ביצה ל”ו ע’ ב’, שו”ע אדה”ז סי’ רמ”ח סעי’ ט’, סי’ של”ט סעי’ א’, ועוד