there sort of is and sort of isn't, searches don't travel a fixed distance through the network then stop so there isn't a horizon like that, but they are replicated through the network randomly, and the further they have traveled so far the lower the chance of being passed on further - so that limits the range it searches based on which primaries it happens to be passed to, and of course the further it travels the lower the chances of it being passed further, so it eventually hits an (undefined) limit and dies off
so there is sort of a search horizon in that it only goes a certain distance, but that distance isn't some defined limit so it's not technically a horizon... (well, actually there is a defined limit, but they rarely reach that far)