The second sentence sounds like a mistake even though technically it's not. In your examples, people expect to hear the "When…" clause as an adverb. However, your second example makes the "When…" clause the subject. That's grammatical but unexpected. There's a little bit more going on here than rules of grammar, which I'll explain below.
Subject vs. adverbial clause
When the boss is angry is a bad time to ask for a raise.
Here, the "when…" clause is the subject. The sentence makes a statement about times when the boss is angry.
What were you thinking? You asked for a raise when the boss was angry!
In this sentence, the "when…" clause functions as an adverb, indicating the time when you asked for the raise. Notice the main verbs: "is" in the first sentence and "asked" in the second sentence.
It was tough
Another factor influencing how native speakers understand your example sentences is that "It was tough" is a very familiar phrase and structure for this kind of thing. "It" here can be understood either as a fictitious subject, so the sentence refers to generally prevailing conditions (as in "It is raining"), or "it" can refer to some specific situation or activity established by context.
It was tough to start a business.
Starting a business was tough.
The first sentence suggests that the prevailing conditions—perhaps the general economic conditions or perhaps a problem with the listener's physical health—added to the usual difficulties of starting a business. The second sentence focuses more narrowly on the activity of starting the business. But either sentence could work where the other could work. There's no rule or precise distinction of meaning here, just echoes of similar phrasings in many other circumstances.
Your second example clashes with both typical ways of talking about an activity being "tough". The echo of the familiar phrasings is so strong, a native speaker wants to add a fictitious "it" to conform to the customary pattern:
When you started a business, it must have been pretty tough.
Your version is grammatically correct, but it goes against the grain of English. What is the sentence saying must have been tough? If starting the business must have been tough, then a person would normally use fictitious "it" or "starting a business" as the subject. If you want to say that the prevailing economic conditions of the time were tough, or life in general must have been tough when you started the business, then the most customary phrasing would use fictitious "it" as the subject.
A tough business
There's another peculiarity about the example sentences: they say "a business" rather than "the business", but they refer to the activity of a specific person: "you". There's nothing wrong with that. However, it's another aspect of meaning to be aware of. By saying "starting a business", you indicate that you are talking about the difficulties of starting businesses in general, not just the specific business that the listener started.
If you change it to "the", the sentence sounds even more like a mistake:
When you started the business must have been tough.
The word "the" focuses on the specific business, and away from the generally prevailing conditions of the time. This makes using the "When…" clause as the subject even more jarring. It's so odd, a reader will likely parse the sentence as if it had a comma after "started", so "the business" becomes the subject. But "When you started, a business must have been tough" pushes the limits of comprehensibility without some unusual context to clarify it.
A difficult subject
More generally, it's hard for English speakers to hear a clause starting with a relative pronoun, like "When…" or "Who…", as the subject of a sentence. It can be done (and it's not as unusual in archaic forms of English), but it becomes especially difficult to hear it that way when the subject-complement is an adjective. Usually, you would add a noun before the relative clause or you'd make the subject-complement into a noun, like this:
When we met was pleasant. → The time when we met was pleasant.
When we met was pleasant. → When we met was a pleasure.
I'm wary of explaining this so abstractly, though. If you think too much in terms of abstract grammatical rules, you don't develop an ear for the language. And this is not a rule; it's just the way people address the fact that a relative clause is easier to hear as a noun phrase if there's an actual noun there to anchor it to.
The moral of the story
Even though in English, sentences like "Times are tough" and "I had a tough time" are very familiar, customary phrasing steers a listener away from parsing a "When…" clause as the subject of a sentence calling a time period or activity tough—even though the rules of grammar allow it.
The main thing to learn from this example is that while the grammar provides many options to say something, experience with similarly structured sentences about similar things often leads people to expect one or two of those grammatical choices and not others—so much, that they can perceive an odd choice as "wrong" even though it's grammatically defensible. It has to do more with customs and familiarity than with rules. The only way to learn these customs is just to get a lot of experience with English. Notice what familiar phrases people are echoing and varying, and you'll understand how they're getting their meaning across.