Give her a good brushing and curry, and then vacuum – it will get that dust and grit out of the coat – because that stuff will make your blades dull quick! I am assuming you do not have a horse vacuum, but even the hose attachment from your house vacuum should work. ]
If you do the hot towel method, make sure she is TOTALLY completely dry before trying to clip – damp hair is the worst to clip.
And yes, able amounts of show sheen (on a clean or dirty horse) will really help the clippers glide through the hair.
Another advocate for show sheen!!! groom as best you can and vacuum if you have one. Make sure you brush off the clippers regularly as the dirt will make them hot and dull much faster so keep them clean and lubed up!!
You are never going to get as good a result on a dirty horse as you are with a clean one, but often the weather and horses conspire against us! Get her as clean as you POSSIBLY can, and if you're wise you will have LOTS of blade lube and an extra set or two of sharp blades on hand. I make sure, if I'm clipping an even partially dirty horse, to have at LEAST 2 sets of blades and plan on using all of them if I have to do the whole horse. Clipping my Shetland is even more challenging because getting her truly clean is really difficult when her winter fur comes in--she's SO woolly and waterproof that the hair never really dries! So I use sheep blades to "shear" the wool and then the remaining coat can be washed and clipped with normal blades.
Clipping dirty SUCKS. I would at least try to shampoo and towel ringe the topline winters to bum and all over the top of the bum. Do the best you can with the rest. Douse, just DOUSE, in Showsheen... and be prepared to dull the blades and look trackier than if you had a clean horse to start.