89 Honda XLT (trouble starting)

Hi again folks

I have an 89 Honda XLT (automatic) that runs great, but with the weather
changes - it's having trouble starting. About twice a week (seemingly on
cold wet mornings) , the choke seems
to not work + It needs to turn over for about a minute before it finally
coughs + sputters to life. It runs once it starts, but still seems to have
no choke so it coughs on occasion until it's fully warmed up.

Is there an easy fix for this, or will it probably be expensive?

TIA

VB