The way I interpret the quote is a warning for businesses that don't strive for long term success.
(since I brought up the quote, I'll briefly mention some context)
Around its time, WCW has probably one of the biggest and boneheaded decisions ever made in the pro wrestling business, yet these were made at the time where WCW was making so much of a killing, WWF (and Vince) were getting their butt kicked with a steel toe boot. WCW, even with the ire of the fans, could afford to make mistakes and with the help of NWO, they could milk as much money as they wanted. In this case, "When the business is hot , you can do no wrong" means that mistakes were doable for the company because of they were successful and still able rake in huge amount cash from their fans. At the time, nothing could hurt them.
However, this would be would not be for so long. With financial success, they had no means to change and why would they? If it's not broken, don't fix it right? This is where the business for the WCW would turn cold. Because of long term fan resentment (as well as other factors), WCW suffered lost ticket sales and low television viewership rations. WWF would soon rise again and the writing would be on the wall for WCW. There wasn't nothing they could do to turn it around. In this case, "When the business is cold, you can do no right" means that because were unable to address the long term problem, they couldn't get their fans to stay with them and inevitably, they were finished.
I brought the quote up in regards to AEW. While I believe its good to have competition, it still worries me to see a company throw down with an iconic pro wrestling business such as WWE. Lest we forget, TNA grew way to quickly and lost its momentum as soon as it started to directly competed with them.
You are correct that "WWE is the business", but i would argue that it isn't the business it once was. There have been some good improvements over years (NXT, acquiring more indie talent to WWE, Women matches getting better quality matches, to the point where they are in the main event of some shows), But their have been many MANY bad decisions over the years (Ruining the Nexus, Bringing back older talent to bury new talent, Backstage politics, NXT used briefly and then made into cannon fodder, "Baylay, This is your life" Segment, Vince's decisions and favoritism, etc). That is just to name a few and no doubt, we could make a list of WWE's short comings and it would take up the entire page of this thread.
Do I want WWE to fail? Well...no and I don't want AEW to fail either. As the saying goes, those who do not learn from their history are doomed to repeat it. Since its recent conception, AEW is ready to charge into battle. Whether this is sheer confidence or bitterness, the company has gained a lot of support from the fans. I'm hoping it does well, but i am concerned how they will go from here.
TL:DR - Business can be hot/cold in terms of financial gain. If Vince is still getting a ton of money with bad decision, then it would be considered hot. However, the other companies are getting hot as well, with AEW being the as hot as the Lut Desert. The way i see it, It is Vince's short-sightedness and out of touch demeanor that keeps it that way. The muscle bound hero that always wins, like Hulk Hogan, John Cena and Roman reigns (when he was heavily booed) has been done and fans are tired of it. Yet, Vince still presses the idea regardless as it is his guy. Thus, wrestlers are stuck under a ceiling made of plexiglass. Keep in mind, when i say that the business is cold for WWE, this is the result of many many poor decisions and the refusal to change or adapt for the long term.
[As a side note: If anyone is interested in The Death of WCW Book, I recommend it. there is so much detail in the book I haven't really touched upon. Give it a read, you wont be disappointed.]