music in 4/4 is usually defined by what happens on beats 1 and 3 (the down-beats)
snares on 2 and 4 are known as back-beats and are the hallmark of most pop music using drums - the flow of accents in the bar are broken by the use of both downbeats (kicks) and back-beats (snares)
that said, a snare can hit anywhere you want it to as it provides rhythmic push/pull - think of the tracks you like and then listen/analyse what the snare does over several bars - you should find that it probably always hits on 2 and 4 but it also has hits off-the beat at the 8th or 16th - this creates interest and movement, both useful for making a track more listen-able
going over the top and only playing snares off-the-beat may be novel but will quickly wear thin and loose you listeners - as with anything we do, meeting the expectations of listeners is far more important than breaking those expectations with novel twists and turns