Synchronized led blinking in multiple boards, wirelessly controlled

I want two or more boards (less than 50m range) to generate a LED blink at same time, within 1 ms difference, using wireless communication. My idea that one of the boards will just broadcast a synchronization signal (say every minute). The both receivers will blink LEDs based on a set time interval (say each second), and whenever the receivers get sync signal from the broadcaster they will blink. Thus the outputs are synchronized every minute.

Will Arduino boards be good enough for preliminary testing? I would like to know how feasible is it to get less than 1ms synchronization. Also, what kind of wireless transceiver should I use? Because later I to want to make a small size and low power boards.

It's feasible. One boards sends a ping to which the other board replies. The first board measures the time between sending and receiving the pulse, divides it by half for one way trip and applies the offset. Assuming that the sending and receiving code is the same on both boards (takes the same amount of time) it should work.