How can I determine if there's a statistically significant difference between distributions in 3 groups?

I have 10 sample zones. For each zone, I have data for about 1000 parcels reporting the %of grass, shrubs and trees within the parcel. My 10 zones belong to 3 broader categories. How can I test whether there is a significant difference between these categories ?

[EDIT : so I only have 3 - 4 zones per category]

It's not clear what you want to test. Are you interested in comparing the probability of belonging to 1 of 3 categories or some other quantities between these 3 categories? Either ways, if I understood correctly, you have a large sample of 10 zones x 1000 parcels = 10,000 units, correct? If each of your categories is also large and you can assume each parcel is independent of the others, you can use the central limit theorem and do pairwise comparisons. But keep in mind that you will need to adjust for multiple hypothesis testing because you will make 3 pairwise comparisons. A Bonferroni correction for 95% confidence is $1 - 0.05/3 \simeq 98\%$ i.e. to reject the null, you need a p-value that is smaller than 0.02.