Warm nose in dogs indicates nothing but hard tummy and foamy vomiting can be due to canine bloat. For details, visit this link.
Toy Poodle Vomiting Yellow Foamy Stuff, Warm Dry Nose And Tummy A Little Hard-what Does This Mean?
My German Shephard had this a while ago, we realised that it happened when she had eaten a rawhide on an empty stomach, sometimes when they eat stuff that doesn't settle it will create Bile which is the yellow foamy stuff. I gave mine some lighty scrambled eggs to settle her tummy and fed as normal when next feed was due, she was fine after a day. Hope this helps
Your dog might be having canine bloat which causes foamy/white vomiting along with shaking due to abdominal pain. For details, visit canine bloat.