Three out of four of my dogs are neutered. Not one is fat or has a poor coat.
Exercise and correct amounts of food will sort the fatness - a great deal of dogs do not do anywhere NEAR a sufficient quantity of exercise per day and most are overfed, in fact the recommendations on the sides of dog food packets are often up to 25% MORE than the dog actually needs.
Coats will come right if looked after properly, that means grooming right down to the skin, removing dead undercoat regularly, making sure the diet is good for the skin, and NOT having your pet clippered off.
A lot of dogs who are routinely clippered or shaved almost bald are supposed to be hand stripped, ie the long dead hairs plucked out by hand. Those breeds include spaniels, setters, westies, wire haired fox terriers, schnauzers..... but basically pretty much any breed especially those with wire hair, can be stripped.
The difference is this. Stripping removes the oldest longest hairs, it then allows the new hairs to lie close to the skin, protecting from heat, cold, wind and wet.
A long coat will become 'open' and will tend to eventually curl in some breeds including border terriers, spaniels etc. When this happens the coat is so open it lets IN heat, cold, water, wind etc.
If you shave the coat off instead of stripping you ONLY shorten it. You do not THIN it and thus whilst shorter, it still remains open and will end up softened further by the clippers, and so grow back curlier, more open and less heat/cold/weather proof.
So neuter your pet, feed appropriate and groom appropriately adn dont be tempted to take shortcuts such as shaving, as that will only ruin the coat more.
She didn't ever get underweight, the fact was she got so poorly during her seasons, she only ate, slept and wanted little exercise - she just tired out so easy - so was a little overweight if anything. The weight's crept back up a little recently, but it is 6 years on now, and she's an old lady (with a penchant for maltesers). 
