Nope. Frost has nothing to do with the leaves dropping or colouring.
The tree decides when it has coloured up enough to signal the leaves are done with and then drops them.
Leaves start changing colour when the days start getting shorter and the nights cooler, not because of frost.
My acer has usually coloured up well every year for the past 20 years, except where there has been an extra-early frost or heavy wind and/or rain.
In autumn the days start getting shorter and there is less sunlight. This is a signal for the leaves to prepare for winter and to stop making chlorophyll. Once this happens, the green colour starts to fade and the reds, oranges, and yellows become visible.
Cool temperatures, particularly at night, combined with abundant sunlight, promote the best leaf colours. Freezing conditions destroy the machinery responsible for this change, so early frost actually means an early end to colourful foliage!
So an early frost will
end colourful foliage and cause leaves to drop
before they change colour.
The best weather for brilliant autumn foliage is a growing season with ample moisture followed by a dry, cool and sunny autumn with warm days and cool (but frostless!) nights.
Heavy wind or rain can also cause the leaves to drop before they fully develop their autumn colour.