WHy do you even need 3 beams? Just use one beam placed at 3 feet. How many people are going to enter a garage by stepping higher or crawling under a beam that they can't see placed at a height of 3 feet? I don't know any cats or dogs that are taller than 3 feet, nor any reasonable birds that are taller than 3 feet, hop higher than 3 feet, or attempt to take flight inside a garage. Then, you coud also use a pyroelectric sensor that would only turn on the beam when something was detected to reduce false alarms from snow and hide the beam even more. Or, you could have both on all the time and both have to trigger for an alarm to sound.
Don't use ultrasound. ACtually before I say that, I don't understand what you mean by rate of change. A ranging sonar is not reliable enough or accurate enough in those conditions to do something like that. And if a car blocked the lasers, why wouldn't it block the ultrasound? Also, no ready-to-use ultrasound that I can reasonably get my hands on is operational across that temperature range, nor outside...during the rain. THere are a few, but they have some fancy driver circuitry behind them (they are electrostatic, see) which isn't overly readily available. If you're curious, go to SensComp.