We know that Hops were a big thing in Farnham during JA's lifetime...it's mentioned in contemporary accounts right through the eighteenth century. This quote is from my 1820's Atlas notes on Hampshire.
".......a great proportion of the parishes eastwards of Alton, and bordering on Surrey, is appropriated to the growth of hops, the plantations of which have greatly increased of late years, thought the reputation of the Farnham hops."
Now Chawton is immediately southwest of Alton, but even if it didn't have hopfields, JA would certainly have recognised them! The atlas goes on to talk about the fact that Hampshire is "has more wood than any other county, especially oak". So I guess tht oak coppicing was used for the hop poles, too!
Below is a link to a Kent website with pictures from the fifties showing how distinctive a hopfield looks. No pictures of the Oast houses(Hop drying kilns though).This site claims that the first Hopping Trains were 1844...... Since hops are a vine, they are strung..and hopfileds all over Europe look like ENORMOUS grapevines. There's also a song about "Hopping down in Kent" (Shirley Collins and the Albion Country Band?)
HERE is a postcard of an Oast house typical of Kent. . Modern hopping techniques are shown in some very interesting pictures at this site- which is www.hopmania.com
Some other thoughts....
Hampshire was famous, according to my Atlas, for sheep breeding and pig farming. I do find it interesting that JA mentions oak trees more often than any other tree, that she has such a strong connection to woods in all her novels, and that of all the agricultural products she mentions the one that seems to be used the most is -Pork!