Boxford running slow,playing about with motors and belts is NOT the solution,and a well lubricated Boxford will run in very cold conditions ,the problem is that the headstock will not rotate correctly,so do something about the spindle before the belts or motor are ruined, the lathe is pushing 50 years old and its about time the spindle was stripped the bearings washed out and fresh grease applied,its not a mangel or lawn mower its a precision spindle that requires care and maintenance. It must be in poor condition for it to nearly refuse to turn when cold, Many readers well past retirement must remember wintertime in factory workshops where a pullover plus a jersey then an overall was the norm,and the heating minimal ,the Boxford in the factory where I worked was new in the early fifties and very often ran all day probably averaging 25 to 30 hours per week ,of course in the early cold mornings nobody switched a machine on at full chat,it was switch on at a reasonable speed for a few minutes,and there were no problems with the Boxford on very cold days,when it was at least twelve years old the headstock was stripped and washed out and greased,as a precaution ,it gave good service and was an excellent machine. On machines with enclosed lubricated headstocks and gearboxes ,if they have pumped lubrication it is ok to run them slow for a while,if they rely on splash lubrication then on a cold start they should be run at a reasonable speed to ensure the oil splashes everwhere.
I think the younger generations are nowadays too used to machines /appliances which run for a specified life with no maintenance,who last used a grease gun on a car? Most small machine tools used by modellers are based on 1940/1950s designs which required regular care and a fair amount of mechanical knowledge on the part of the user,they do not run for ever.