Lead solder toxicity after cooling?
The solder does not change- the vapor pressure of lead increases with temperature but the amounts involved should still be pretty small for casual soldering. 

Handling solder wire or PCBs with solder on is not so bad, though you should not do it when you're eating (especially acidic things like oranges- messes up the boards too). Washing your hands after handling solder or soldering is a reasonable precaution. 

If you have a really crummy soldering iron or gun that gets excessively hot, not only will it damage PCBs but you will get excessive lead fumes. This might be an issue for 3rd world scavenging of parts using a propane torch or whatever (then you're getting nasty fumes from the epoxy and other stuff too).

The real danger is solder paste (used in SMT assembly) that you could accidentally spread on a Carr's water cracker in place of liver pâté. More seriously, it can get on your hands (under fingernails too) or clothes and be transferred to your mouth etc. since it is basically tiny balls of solder in a sticky gooey liquid. 

Of course these dangers are greatly increased if you are with a child (they put all kinds of things in their mouths), and especially, if you are 'with child' (aka pregnant). 
Pb-free solder should be safer, but I would suggest still taking reasonable precautions.  

As carveone says, breathing flux fumes is nasty- even good old rosin (eg. Kester 44) seems to stimulate asthma (it does in me), and the lead-free stuff needs more aggressive flux. I've got some rolls of solder from China, and have no idea what the flux contains. It's quite safe when it's cold, but aggressive chemically (by design) when hot. 

Here's a fairly thorough look at the hazards of (wire) soldering done by a University (many of us have done things like this for companies, but they're not generally publicly available). It includes such useful suggestions as not touching the hot end of a soldering iron.