Do you need to actually add a new field to the shapefiles themselves? Or just add it to the read-in structure in Matlab?
If the latter, you can easily assign new fields and values to your structure
India = shaperead('~/Downloads/shp/naturalearth_india_adm1.shp', 'usegeocoords', true);
for ii = 1:numel(India)
India(ii).rain = rand(1);
end
You can plot shapefiles colored by a property by using the (extremely clunky, IMO) symbol spec parameter to geoshow:
spec = makesymbolspec('Polygon', ...
{'Shape_Area', [-11 31], 'Facecolor', parula})
geoshow(India, 'SymbolSpec', spec);
In this example, I've used the area of each polygon as the color-mapping data, but you can adjust it as needed. The down side to this plotting method is that the colors don't correspond to the colormap at all, so you need to manually sync your color limits to match the spec if you plan to use a colorbar or plot other data on the same color scale.
If you need more control over the output, you can instead plot without the symbol spec and set the CData property of the resulting patches:
h = geoshow(India);
set(h.Children, {'CData'}, {India.Shape_Area}');
set(h.Children, 'Facecolor', 'flat');
Using this method will link the patch color to the axis color limits and colorbar. Which behavior you prefer may depend on your application.