paulbates

It was me, not UDI. I was writing a program that resulted in a tight loop with many UDM push notifications.
My bad and apologies to UDI and this community
Paul

The reason it's happening is that you want to know if either is triggering, and they both are at slightly different times. 
Assuming they're both triggering within 5 minutes of each other, I would do it with a timer and a second program
Program freeze warning 1
If 
    Your first weather condition
     Or Your second weather conditon
Then
     Run program freeze warning 2
else
 
Program freeze warning 2
(no if)

Then
       wait 5 minutes
       Send notification 'xxx'
       Resource 'Freeze warning message'
else
 
When the second conditions triggers, the second program will restart because it's waiting, and you'll get only one message. Start with 5 minutes and then try reducing the wait time so there's not as much wait, but the program continues to run only once
 

It's a feature that was more important in the early ISY product days. The ISY has a web server in it and can serve up web pages, including web pages to control ISY devices and programs. HTML role has options for how much of that control you want to give a web user of your ISY.
I don't believe it has relevance in the era of plugins and mobile apps. It does not affect the Admin Console. FWIW I leave mine on advanced on the outside chance something happens and I have no other way to reach my ISY. 
From the ISY 26/99 wiki:
HTML Role:
Read Only - Allows Program status to be read. Basic - Allows Programs to be Run (If), Run Then, Run Else, and Stopped. Advanced - Allows the user to Enable/Disable Programs. Admin - Allows the user to Enable/Disable Run at Startup for Programs.  

No. It's not designed to run continuously.

I've recently purchased and installed it on the version prior to 5.8 and it installed as it should and working.
So I'm going literally by the steps you listed, I don't see that you did the install step? That would explain the outcome. Install and reboot
If that's not it, I would go to the pg3x log, set for debug and look at the entries near the bottom for errors related to yolink.

You can do it by storing one of the devices temperature's in a state variable in a program:
If
  Device_Node_Temp not equal State_Var_Temp
Then
  State_Var_Temp = Device_Node_Temp
 
The you can create the program to control the wine cellar by comparing the other device node temperature reading with the variable with the temp variable. There's a tiny arrow head at the end of the line when building the if statement next to the device node you've picked... click it and a list of variables will come up. 
It has to be a state variable for the if statement to function

It should be possible... Use the "schedule" clauses with AND and the other device conditions.
It's hard to be more specific without more info or a sample program you might have started

This is not exactly what you're asking, but there are other ways to debug
Put notifications in key spots in programs to alert you and then remove them once the program is working. I've recently completed several programs and notifications got me around my "bugs"
  As an alternative to notifications, set a variable, If your program is setting variables this is a good method and also recently used this method. To see these changes, open the event viewer (as opposed to the log) and look for entries something like VAR[ 2 7]... where 2 = state variable, and 7= variable number on the list of variables.
   

Looks like you're on an isy 994i. The new insteon i3 devices are not (fully) supported, you'll need a polisy or eisy to fully utilize i3 devices

The combination of older PLM and flaky behavior says it's time to get a new PLM and handle the swap on your terms, not when things get a lot worse and it stops working.
 

Also possible-to-likely is that the new router's ip4 subnet is different than the old router's.
Via the mobile app:
Settings Systems Pick your isy Scroll down to "local connection settings" Your ip and ports will be listed there