Is it OK to lay asphalt in the rain? The contractors are here waiting for the hot asphalt. It is 41deg outside and looks like it may rain anytime. They say it'll be fine. Yeh!!

Not a great set of circumstances for sure, and the life of the pavement will be affected to a certain (maybe only slight) degree. My experience is in inspection of highway construction and we encountered situations when it was necessary to do hot mix asphalt (HMA) paving in the rain. The effect just based on my own observations was that the pavement still performed pretty well.
One of the primary concerns with placing HMA is that the rolling (compaction) must occur before the asphalt cools down too much. With temp at 41 deg. And rain causing more cooling, temps would be my biggest concern. Criteria at one time was that the mix not be below 180 degrees F before rolling was completed. Rolling at lower temps can cause cracking instead of compaction.
Depends on what surface the HMA is being placed upon also. If the HMA is placed on stone or a dense graded crushed stone mixture and that base material is saturated, it may be impossible to obtain proper compaction and/or the surface may be distorted by the roller. If placed upon an existing asphalt or concrete pavement, heavy rain will cool the mix quickly and affect the bond, but a very hot mix can literally boil the water away..
Very generally speaking, if the HMA arrives hot (ours had to be min. 325 degrees), and is placed on a firm base and is rolled before it cools down below 180 degrees, a light rain and a temp of 41 degrees probably won't create an unacceptable pavement.
The big difference here is that we never started placing HMA if it was already raining, just when caught in the middle of the job unexpectedly.
State specifications used to require that paving be suspended from Nov. 15 through April 15 every year. But that delayed completion of and/or public use of many nearly finished roadways, so it is looked at on a case by case basis nowadays. Rain does not affect HMA nearly as much as cement concrete pavement which is definitely damaged by rain weakening the mixture, and especially the surface.
If it wasn't a heavy rain, the mix arrived hot, rolled before it cooled off too much, and paving equipment and delivery trucks didn't rut the base material, the pavement should do well.