I did a little digging in regards to Harry's uniform.
Again based on this picture:
https://fbcdn-sphotos-d-a.akamaihd....407_739874852701014_2054094358844194209_o.jpg
Harry is wearing the no. 3 dress uniform of an officer in the Household Cavalry.
The guards regiments have a no. 1 dress uniform, which is the standard dress uniform. (Full dress with sabre and medals). And to supplement that they also have a no. 3 dress uniform, which is the summer/warm weather variant - and that's what Harry is wearing here.
All other British regiments (i.e. non guards regiments) only have a no. 2 dress uniform. And that's what you see the Royal Air Force adjutant, (as well as the Estonian officers) wearing.
If officers in non-guards regiments wish to wear a no 1 dress uniform, they have to pay for it themselves and in any way that will only be required rarely. But officers in the guards regiments, with the additional official functions they have, must have a no. 1 dress uniform. (With a no. 3 dress version as well).
If Harry is going to Estonia to honor those who have fought and fallen alongside British troops as the primary function, then it's most natural for him to wear the clothes most appropriate for that particular event. I.e. a uniform.
If Harry was there for a primarily civillian function, like an official visit or a diplomatic mission, then it would be more natural for him to wear civillian clothes. - But there is actually nothing to hinder him from wearing a uniform all the time, because he is entitled to. Even to the cinema, if he wished to. (That would be his no 2 dress uniform BTW).