What does Tigger eat, and when was her last check-up at the vet?
Skin and coat condition is often a reflection of health, so I'd be concerned that this is more than just something to do with dry air. If Tigger hasn't seen the vet within the past 6 months to a year, it would really be a good idea to have a senior blood panel and urinalysis done. If the results of that are normal, perhaps a re-evaluation of her diet is in order. As cats age, their nutritional requirements can change.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler