Any more info about this? When was this freehand have occurred?
Well, Metternich wanted to reform the Monarchy after the Congress of Vienna. It's hard to tell precisely, he was perceived as a reactionary (and he
was in foreign policy, lambasting liberals for trying to adopt the British model), but he did clash with the Emperor repeatedly over the Emperor's autocratic rule. I'd say he was pragmatic more than anything, concerned with the internal stability of the Empire and seeing the reforms as one way to do that.
I'd say that any time between 1815 and 1826 would allow him to reform the Empire to his liking.
The unofficial regency (between 1835 and 1848) of Ferdinand I (of Austria)/II (of the Holy Roman Empire)/V (of Hungary) was riven with factional disputes (Kolowrat was a long-standing rival of Metternich's and Archduke Louis favoured absolutism) so the status quo was maintained. A status that favoured Kolowrat and Louis, as Franz I had established absolutist rule quite thoroughly.
Kolowrat wasn't in a position to interfere before 1826, being in Bohemia and holding no political office in Vienna itself. So, having Franz I die before then would allow Metternich to control the Empire (it doesn't solve the problem of Louis, but alone he's less of a problem).
However, this is all outside the scope of your request. Though I suspect the changes wouldn't affect the military, allowing Prussia to win nonetheless. Everyone else in Europe thought the Austrian military should be able to beat down Prussia easily (including quite a few Prussians), anyway, so I doubt the military would be reformed more than it was.
The effects on 1848 would be a lot more significant, however. The internal chaos of the year would probably bypass Austria (or, at the least) be reduced given the autonomy and democratic institutions Metternich would have instituted. Which means Metternich stays in power and Ferdinand I doesn't abdicate in favour of Franz Josef (though, given the severity of the Emperor's epilepsy, as many as 20 attacks per day, it's only a matter of time before he kills himself by accident).