He couldn't have done much; he didn't have much influence outside his royal connections. He was not received by President Truman for example. You probably know of the famous distribution of power after the WWII among the allies. Romania was 90% under the influence of the Soviets.
In the first years of the exile he supported a phantom government. He kept touch with all that was happening in the country, as much as he could.
While in exile he kept a low profile, a sort of an "austere" live, in order to be in solidarity with the sufferings of people and the country.
I remember hearing each January 1 the king's speech to the Romanian people on Radio Free Europe and hoping for better times.
Is it much, is it little? Who can judge?