Welcome to the forum. NO, the letters T and W are merely fitters marks and have no significance outside the factory. The letters and numbers in the yoke area are assembly numbers and were used back in the day when certain parts were hand fitted to the gun. This includes the side plate. That same yoke number will appear on the back of the side plate if original to the gun. These numbers were needed to get these fitted parts back together after the gun was disassembled for finishing. Once the gun was finished, either blue or nickel, the numbers helped get these fitted parts back on the gun.
Guns can be refinished without overly disturbing the words and numbers by a quality re-finisher. These letters and words can also be re-cut, so this is not necessarily a good way to judge a refinish.
As my learned colleagues have advised above, poor fitting side plates or ones with rounded edges at the seam, plated hammers and triggers, platted extractors or flattened round pins are some of the others things we look for.
There are many guns out there that were done in the style of your gun with steer head stocks and bright nickel finish and as someone stated, these guns are referred to as barbecue guns. Merely having the steer head stocks would raise a flag to me that the gun might be a refinish.
It's a cool gun and may have some LEO history but remember you are buying the gun and not the story. Unless a very famous person once owned it or it was at the OK corral, there is no added value.
