I have only had personal experience putting on lambs of up to 2-3 days old when lambed outdoors "on the hill" of a farm in the Scottish Borders. Any older, they should have a reasonable fat covering, be able to go and hide out a rainfall and use the heat they gain from burning the good supply of mum's milk to stay warm. The main problems are more wind than rain, as this can chill where rain doesn't, so as long as there are plenty places they can hunker down behind walls or hedges or bales of hay/straw/manmade shelters they should be fine. In terms of rejection, after about 24-48 hours, the recognition between mum and lamb is more by voice than smell, it's usually if another ewe licks within the first couple of hours of birth that the mum will reject it.
Hope that helps
Suzanne