I have half an application filled in on the
http://www.planningportal.gov.uk/ with my plans drawn up ready to go. I am just waiting for another planning application to go through prior to that as its not covered by that act (its a toilet block so not agri) and dont want to let anything jeopardise that app as its more important to me and is proving harder to get.
In my opinion the act was written to help smallholders/farmers not get wrapped up in long and complicated planning applications for building things that are a necessity and not a luxury, it allows for farms to expand to fit the modern needs of farming. (which is why you need the acreage)
The one thing that comes to mind though is that I am pretty sure that any new builds under this act cannot be for the sole use of animal housing, more storage for modern equipment, dry storage for food stuffs, vehicle maintenance garage, you also have to write in your application why you need this space and as has been said ponies/horses are not agricultural even though many make up vast parts of rural life, livelihoods and events. etc etc
If you have a receipt for the documents and they have been accepted as a formal planning ap then I'd go ahead and start as they have not got back with an objection. - But it does sound like you have not submitted it through the correct channel or in the correct format for them to accept it as a planning up under this act. They could be stalling you for this reason.
I have a feeling that all they are going to advise you next is through what routes you need to start applying ie under the above act or through the normal planning routes.
In all honesty after all the waiting for planning I've had, I wish I'd just build it and gone through the plans later. Every year my business plan gets put back due to lack of infrastructure, its a year of continuing with the losses of not having the infrastructure in place to expand the business. If it takes another year for the plans to go through then I may of well have taken the risk of building it in the first place cos it cost more in 'lost' business revenue than what the build cost is. - rant over

Ta
Baz