Jingle Bells lyrics - what does this mean?

Now the ground is white
go it while you're young
take the girls tonight
and sing this sleighing song

Just get a bob-tail nag
Two forty for his speed
then hitch him to an open sleigh and
crack, you'll take the lead.

What does "get a bob-tail nag, Two forty for his speed" mean?

The bobtail part just means the horse's tail is cut is docked, or chopped so it will stay short, which is done in carriage horses to prevent the tail from getting tangled in the carriage or reins.

"Two fourty FOR his speed" may mean a mile in two minutes, forty seconds, which is about 22.5 miles per hour. If you've seen our Horse Speeds in MPH chart, you know that's far faster than the typical horse can trot (and horses pulling carriages, typically trot).  This would mean the horse would have to be a Standardbred, a breed bred for harness racing that can trot faster than other horses.

The breed was called the "Standardbred" after 1879, because the horses were allowed to be registered if they could trot a mile at the "standard" speed, which was 2 minutes, 30 seconds. All Standardbred horses today trace their lineage back to Hambletonian 10, a horse born in 1849 that was able to trot very fast and sired over 1,300 foals.

It could also be two-fourty means 240 seconds, which is about 15 mph, or two furlongs in 40 seconds, still about 15 mph -- the pace of a normal horse trotting fast.