Why is a 737 Original speed-restricted below 10 kft with inoperative windscreen heating?
To reduce damage in case of a bird strike.
The restriction is not only for the 737-100 and -200 models, the 737 NG QRH says:

WINDOW HEAT OFF
In flight:
WINDOWS HEAT switch (affected window) ..... OFF
Limit airspeed to 250 knots maximum below 10,000 feet.
Pull both WINDSHIELD AIR controls. This vents conditioned air to the inside of the windshield for defogging.

The reason for restricting the speed is that the windows are less elastic at lower temperatures and can therefore not absorb a bird strike as well as at nominal temperature. Since most bird strikes occur below 10,000 feet, the restriction only applies there.
I could not find a good source for this, but it is e.g. discussed on pprune.org:

Window heat also ensures the screen vinyl layer is kept elastic and resilient and better to absorb damage in case of a bird strike - not so if the screen is cold and hard.

and airliners.net:

cold windows become very brittle whereas warm windows have a degree of elasticity in them that makes them withstand birdstrikes better.

A new window was developed for the 737 and is installed on all models built since mid-September 2010. The technical data by PPG Aerospace list the following among the improvements:

Elasticity at low temperatures reduces potential for delamination and cold chipping

So low temperature elasticity seems to be improved. I do not know, if they removed the restriction from the QRH for the newer models.
Airbus also does not seem to have such a restriction. From pprune.org:

When I asked Airbus exactly this question their reply was that the windscreens had been tested at 350+ knots and cold.....therefore no problem!