I pick before I ride or anytime I groom. My horse has shoes on all fours and has a long stride at the walk as it is. Even with bell boots you can hear the occasionally clinking of his shoes together at the walk. Because of this I check to make sure his shoes are in order still. Also I live in the rainiest state in the US so he is in mud for about 10 to 11 months of the year so picking is a must to keep thrush away.
As much as I can- daily, before a ride, after a ride, etc. Its a skill that used to terrify me, so I take a little pride in knowing that now its the one grooming exercise that calms me down. That, and if my gelding is being testy that day, I can usually tell by now eager he is to cooperate with hoof work.
A horses hooves should be picked out everyday - at least* Grooming is a great time to carry this out but also before and after every time you ride and turn out, the reason for this is that every time your horse moves around, whether it be on a riding school, a grass paddock, a dirt track, a road ect, its hooves are at risk getting a stone or a piece of wood chip wedged in it or having wet mud, sand of even feaces or urine soaked shavings from its stable compacted in it, so imagine that you do go to the effort of cleaning your horses hooves before you ride, it has a lovely gallop through a field but its hooves become full of wet mud and stones and you return it to its stable after your ride thinking "its ok, I have already picked his hooves out" but what you don't realise is that now your loyal little has to stand in its stable for the next couple of hours, or even over night, with with wet muddy/stone filled hooves. Imagine if it was the other way round and you had to live with wet mud and stones in between your toes.