Why do some aircraft require anti-icing on the tail while others (Dassault Falcon Jets, Boeing 737, 747, etc.) don't?
Some airplanes don't need the horizontal stabilizer to have anti-ice because it was shown during flight testing that there were no adverse effects from having ice on the tail.
This is mainly because the horizontal stabilizer/elevator has been designed so that even with a degradation of lift due to the ice, it still produces a sufficient tail down force to maintain control, even when approaching the stall speed.
The airplanes that do have anti-ice usually either have smaller horizontal stabilizers or (on some older designs) couldn't get the FAA to sign off on a design without it. Some designs are also more prone to collecting ice (based mainly on the radius of the leading edge) so must demonstrate sufficient handling qualities with even more ice, which may not be possible.
I would expand a little bit more the answer. Firstly you are talking about anti-icing systems. Actually there are 2 kind of devices that provide protection agaisnt icing, from one side the anti-icing systems, like heaters, and de-icing systems, once iced is created the systems destroys it. For example, F17 used de-icing boots on the horizontal plane, so it was not using anti-icing. ATR72 is another example of de-icing systems.
However, I think your question is actually why some airplanes are not using ice protection systems (both de-ice and anti-ice) on horizontal planes.
The answer is clear: because is cheaper to have a bigger tail.
Let's recall what's the horizontal plane is doing, its function is basically providing balance to the airplane and supporting maniouvres in flight, like for example take-off, recover from a failed landing...
When designing an horizontal tail plane you need to consider all potential maniouvres that the plane needs to answer to. One of those conditions need to be possible with the presence of ice or having a system avoiding having ice.
So, to provide the same performances, either you have a system that avoids having ice or very few or you have a bigger plane. On top you have other conditions which are dimensioning the plane, like flutter or other maniouvres.
- Either was lighter having a bigger plane that operates safely with ice than a smaller plane with ice protecution
- Or there was another condition in the design that was already making the plane big enough to operate safely with ice, making the ice protection system not mandatory and so not needed weight.
To be honest, I can't tell you for each airplane which was the dimensioning condition that eliminated the need of ice protection.