Both titles "Happy Tree Figures" and "Dick Tree Friends" and how the "show" is supposed to work out are played on Dick Figures, another popular series by Mondo.
This is the second April Fools joke for Happy Tree Friends. The other was when Lumpy won Vote or Die.
Also, the thumbnail for this video is the same as that video for an unknown reason, possibly a reference to the upcoming episode (Royal Flush). It could also be to trick the viewers as if the video will be about Season 4 with an episode starring Lammy & Mr. Pickels (which is what the upcoming episode will star indeed).
While in their Dick Figures forms, Toothy didn't have his tail, Flippy didn't have his ears, and Cuddles didn't have his tail.
According to this episode, Giggles is the first female character to appear in an episode with clearly visible breasts. Also, Giggles is the third character and first female character to smoke in the series (after Pop and Lumpy).
This is the only episode where a character is killed with a firearm, despite the rules of no firearm kills. However, it could be possible that they gave firearms in this short because of the different animation style and the different theme; HTF is colorful and gory, while Dick Figures is simple and raunchy.