NO – sorry. I know this is a disappointing answer but the reason it is not covered is important to understand. First, your Homeowners policy is primarily concerned with insuring real and personal property – your home, other structures, and personal property. Any coverage afforded to “trees” is incidental to the policy.
Under ADDITIONAL COVERAGES, 1. Debris Removal, the typical Homeowners policy will pay up to $500 for removal of tree(s) felled by the peril of "Windstorm" BUT only when the tree caused damage to a covered structure. So, in the question above, a big tree blew over but didn’t damage a structure so no coverage can be provided.
There are other very practical reasons that coverage for trees is limited or not provided. Trees, after all, are living things with a life cycle. Disease, drought, or other cause may kill all or part of a tree. If insurance covered the cost to remove fallen trees there would be no incentive for home owners to remove dead trees from their property. They would simply wait for the next windstorm and call their insurance agent for coverage. Also, some home properties include acreage with a forest of trees. Insuring items like trees that can lead to numerous and extremely common claims would cause premiums to rise for all Homeowners policies.
For answers to related questions click: Wind Damage ~ Am I Covered?