I once asked a neighbor with several dead pine trees why he hadn't had them removed. He said he wanted to wait to see if they come back in the spring.
I've always tried to make "dead-tree analysis" simple. "If it's brown, take it down."
You don't always need a tree doctor to come out and tell you if a tree is dead. While there are a few exceptions to the rule, if a tree's leaves are 100 percent brown, or if a pine tree's needles are 100 percent rust-colored, the tree is dead, and it needs to come down soon.
There are three reasons why you shouldn't put off having dead trees removed. First, a dead tree could fall on its own or due to winds, so it is a safety threat to nearby houses, fences, garages, automobiles, etc. If an insurance company can prove you knew for some time that a tree was dead and didn't have it removed, they may not pay an insurance claim for damages.
Second, a dead tree falling among other healthy trees can damage those trees, ripping off branches and gauging trunks.
And third, it may actually cost more to have a dead tree cleared away later because removal becomes more intricate with decomposition. In a tree's early stages of death, it is solid enough for an expert to climb and remove it one section at a time. When it's rotting, no one can safely climb the trunk, so the removal process requires more equipment, more workers, and costs more money.
So, if it's brown, take it down ... immediately!!!
How do you know if a tree is struggling to stay alive? Many trees are starting to shed leaves for the fall, as they normally would. However, trees shedding yellowing leaves prematurely are likely having problems and could benefit from deep-root watering and feeding. I encourage you to do it on your own, but older trees need treatment by a professional. Be careful, though: price-gouging tree companies come out of the cracks this time of year.
Be sure you're getting a good deal from a certified tree company. The cost of tree removal depends on the size of the tree and its ease of accessibility. Call at least three companies for bids. Price-gougers will overcharge because they think you may be trapped. Uninsured companies will give you the cheapest bids because they don't have much overhead. However, "rational" bids will never be the cheapest or the most expensive. Affordable Tree Service at 713-699-2663, a company I have endorsed for years, is a good example.
Any tree company that bids your project should provide proof of liability coverage and workman's compensation insurance. If they can't or won't, don't hire them. If something bad happens due to a fallen tree, it'll all be on you and your insurance. Don't let Murphy's Law take part in your removal.