Guru Gobind Singh held the first mohalla at Anandpur in the spring of 1701, on the day after Holi. The placement was not incidental and the tradition has never presented it as such.
Holi is a festival of coloured powder, licensed disorder and reversal. What the Guru instituted the following day was a mock battle: two forces, an objective, a column advancing on it to drums, and a review afterwards. The name is built the same way, hola, a masculine form made from Holi, joined to mohalla, an organised march.
The programme is the same one that produced the Khalsa at Anandpur two years earlier: a community given its own forms, its own initiation, its own dress, its own discipline, in place of forms shared with its neighbours. A festival of play was answered with a festival of preparation.
That reading is the tradition's own and is stated openly in Sikh sources, which is worth saying because the parallel case of Bandi Chhor Divas is often disputed. Here there is no dispute about intent. What is sometimes lost is that Hola Mohalla is not Sikh Holi any more than Bandi Chhor Divas is Sikh Diwali; it was constructed as an alternative, by someone who said so.
The Nihang orders, who lead the modern gathering at Anandpur with horsemanship and weapons demonstrations, maintain the martial content the festival was created to house. The crowd is now in the hundreds of thousands.