The running zig-zag argument is such BS. First of all, we're talking about a kid who is what, maybe 8 years old at best? Rickon has no f***ing clue what he's doing. He's just trying to cover as much ground and as fast as he can because he's running for his f***ing life - away from the enemy who has a huge army behind him, the guy who has captured and tortured him, who has taunted and possibly destroyed his family and who took his home Winterfell - towards his brother (a symbol of safety and protection).
Second, again, as a 8 yo even if he was running zig-zag, what's his top speed? Plus, how much mobility and flexibility does he have? He can't just unpredictably cut corners left and right like a bunny. Neither Usain Bolt nor Rickon on the fastest racing horse in Westeros could have fooled Ramsay there. A good bowman, like Ramsay arguably is as a hobby hunter with nobleman training, would have hit him with ease. And if not, Ramsay had hundred+ archers with him. The kid was dead either way.