Now that you know that you should salute the judge, you should. It is respect, just like braiding your horses mane for dressage. Nope, you wont get penalized for not braiding your horses mane, but it is respectful to do so.
You should always salute the judge when you enter the ring for stadium. At Beginner Novice, and at any level. It is the respectful thing to do.
The only time I've seen riders at BN not halt and salute, is when the Judge informs the Ring Stewart to let us riders know when we are entering the ring, that we are running behind on time and to just get on with their round.
I competed at BN last year, and riders who did not salute, were few and far between - most Coaches emphasize to their lower level riders, to salute, to teach them the respectable protocal.
There is nothing wrong with halting infront of the Judge and nodding your head either - so long as you show the Judge that respect.
Well i'm no "official" help as I usually show schooling events only bc I find them more fun and the area here can be really snobby and let's face it, i'm not riding for points or nationals or the olympics - I just want to enjoy what i'm doing!
That said, at any recognized show we ALWAYS salute both dressage and stadium the same way. At schooling shows, it depends on the show. Sometimes we smile and salute-ish, with a nod, sometimes we smile and wave (really!) depending on who's judging. Then again even the one location we show at with USEA eventer Sinead Halpin, we smile and wave, don't braid, and don't even do dressage in jackets but in our polos for stadium and xc... but it's super low key and a TON of fun.
Buuuuuuut to MIE's point, ANY ANY ANY recognized show OR any FORMAL show (some schooling shows are formal) we DO ALWAYS salute. And suit up (jackets lol). Braiding... well i'm still a nonconformist there, hell my jumper turned field hunter turned eventer I don't even pull his mane (sky) but that's just bc we're just badarse ;)