You didn't mention millage on the respective vehicles. That's important.
First, and this is way out there, the '99 has a newer computer than the '97s. As I understand it the maps are different. This affects all kinds of things - one is cold/warm start.
Next, as vehicles get older things degrade. The most obvious is wiring connections and sensors.
A lot more likely are simple things like spark plugs (age and type), spark plug wires, battery, battery terminals, battery cable connections and engine/chassis grounds.
My '97 3.0L Sport was behaving EXACTLY like that for the last several years - irrespective of outside temps. Over the last year and a half I replaced and fixed a dozen problems - all age/use related (KIM, my '97 has 415,000 miles and and the only things that had ever been replaced that would affect starting/running was the battery, terminals and alternator.)
NOW, all I have to do even in 0 degree weather is hit the starter for a second or two - even if it's been sitting outside in freezing cold for a day or two.
In order of things to check:
1) Battery/alternator
2) Battery terminals
3) Battery cable connections
4) Chassis/engine ground connections
Specifically check for large voltage drops 2-4. Make sure the battery is good AND that the alternator is completely charging the battery. APPARENT failure in 1 can actually be 2, 3 or 4 - or 2, 3 AND 4. <img src="/forums/images/graemlins/zombie.gif" alt="" />
Dirty and/or loose connections are the most common and least apparent but always the most likely cause of what you're experiencing. Old and/or undersized batteries are next.
5) Spark plugs/wires
6) IAC sensor - the equivelent of the choke/idle circuit on computer controlled vehicles. BTW, I was told the IAC was improved in '98 or '99 - the testing specs I received for my new one are different that stated in my '97 service manual.
Anything below here would show other symptoms and probably have nothing to do with your question. <img src="/forums/images/graemlins/smile.gif" alt="" />
7) Ignition coils
8) Fuel system
9) ECU
Edward