Check this paper out: Defining Stem and Progenitor Cells within Adipose Tissue. Guiting Lin,1 Maurice Garcia,1 Hongxiu Ning,1 Lia Banie,1 Ying-Lu Guo,2 Tom F. Lue,1 and Ching-Shwun Lin1
I am also interested in finding a way to stain adipose tissue. If you are actually trying to stain the adipose tissue and not just structures surrounding it, it will be important to consider how tissue is fixed, I think.
The authors of this paper have provided a detailed protocol of the Immunofluorescence technique to define more precisely the location of Adipose Tissue-Derived Stem Cell within human adipose tissue. If you are using frozen tissue sections and depending on your antibodies, you should be able to get acceptable staining pictures without significant background. However, you may want to add picric acid in your fixation step with Paraformaldehyde and change your blocking serum. Just check the paper.
Do you want to stain just the vasculature or rather the fat tissue itself, or both? You have also to decide if you prefer frozen sections or paraffin embedded tissue. I would recommend the second if you prefer to have a nice morphology, but it depends on what antibodies you will want to use in addition to the one for morphology. Costainings can be tricky. I would use citraconic buffer if you want to combine several stainings to demask the antigens if you use immunoflourescence.
I have looked at vasculature, innervation and cell proliferation in salmon adipose tissue. The adipocytes are large and quite fragile cels. PFA fixes adipose tissue nicely. Paraffin embedding affected morphology and I skipped using that. Also, for studying vasculature, thicker sections (50 microns and up) are helpfull. This is tricky on a cryostat, so a vibratome would be your best option. Though, you can make hand sections with arazor blade. Embed your tisue in agarose and give it a go ;)
Regarding staining of vasculature you can use antibodies, but even easier is to apply isolectin, whih stains vascular endothelial cells in a short protocol. Also remember to clear the adipose tissue properly before microscopy. Glycerol is ok but 2-2 thiodiethanol is much better. Good luck :)