In the Standard Model as written in the 1970s the neutrinos had to be exactly massless. We now have evidence that neutrinos aren't exactly massless, but they're very VERY light. Like, absurdly light. We still don't know the absolute scale of the neutrino masses, we know from mixing that they're damn small and from cosmology that the sum of all three masses is less than the mass of the electron / a million.
It is logically possible that the neutrino of the fourth generation is very heavy. In that case
- the constraint on the number of neutrinos from collider experiments is relaxed because the ultra-heavy neutrino's contribution to the observable would be extremely suppressed (because the collision energy was too low to be sensitive).
- the cosmological constraints are relaxed because the heavy neutrinos are already frozen out by the time of the electroweak phase transition in the early universe.
- the mixing constraints... well, right now it seems that the mixing matrix between the generations is unitary---there's no "leak" into a fourth generation. But our experimental precision is mediocre because precisely measuring the mixing is difficult (though there are experiments under way). It is also logically possible for there to be a fourth generation but that the neutrino doesn't mix at all---its mixing with the lighter neutrinos is precisely 0. While it's perfectly possible logically, we physicists do not like this kind of "fine tuning" without some explanation of how it could happen. In the SM the neutrino masses/mixings are input parameters, not things determined dynamically---they are axioms, so to speak. So any explanation of the mixing being really small would need to invoke more beyond-the-Standard-Model physics than "it's the same but there's a fourth generation".
It is logically possible that the neutrino of the fourth generation is very heavy. In that case
- the constraint on the number of neutrinos from collider experiments is relaxed because the ultra-heavy neutrino's contribution to the observable would be extremely suppressed (because the collision energy was too low to be sensitive).
- the cosmological constraints are relaxed because the heavy neutrinos are already frozen out by the time of the electroweak phase transition in the early universe.
- the mixing constraints... well, right now it seems that the mixing matrix between the generations is unitary---there's no "leak" into a fourth generation. But our experimental precision is mediocre because precisely measuring the mixing is difficult (though there are experiments under way). It is also logically possible for there to be a fourth generation but that the neutrino doesn't mix at all---its mixing with the lighter neutrinos is precisely 0. While it's perfectly possible logically, we physicists do not like this kind of "fine tuning" without some explanation of how it could happen. In the SM the neutrino masses/mixings are input parameters, not things determined dynamically---they are axioms, so to speak. So any explanation of the mixing being really small would need to invoke more beyond-the-Standard-Model physics than "it's the same but there's a fourth generation".