HaircutsHomeRuffled & Tousled
1. Steed's first sideburns experiment

Steed had some sideburns for the first time during series 3 in three episodes, starting with the episode The Wringer, then in The Little Wonders and Mandrake. Compared to those from series five and six, they were small ones, thin and suited him well, but they were already gone in Trojan Horse.
Steed also has bushy Wild West sideburns in Dressed to Kill, but these seem to be false ones as he has no sideburns at the beginning of the episode.
The Wringer The Wringer The little wonders Mandrake Mandrake
2. At the end of series five Steed started to grow new sideburns and had them until the end of series six of The Avengers.
Series 5 sideburns
the see-through man The winged Avenger the Living dead the 50.000 pound breakfast You just have been murdered Mission ...
Series 6 sideburns
Super Secret Cypher Snatch Invasion of the Earthmen Get-A-Way The Interrogators The Rotters Split!
Invasion of the Earthmen Whoever shot... My Wildest Dream Love all Take-Over Pandora
The New Avengers: Fortunately,elder Steed decided against further sideburns.
Trivia:

longest hair in the neck in The Rotters, longest hair at all in Take-Over.
Steed's Biography 
Sideburns