I think the Smith family and their farming neighbors were one with the land and whatever effects were caused by Mount Tambora in their region would have had an impact. The Smiths were farmers and news of a volcano effecting their livelihood would certainly cause alarm.
Joseph Smith is on record for having interest in volcanos and rambled this off while in Liberty Jail:
Joseph Smith, March 1839 wrote:Hell may pour forth its rage like the burning lava of Mount Vesuvius, or of Etna, or of the most terrible of the burning mountains; and yet shall “Mormonism” stand.
Joseph Smith took interest in volcanos during his life:
Joseph Smith, Letter, March 1843 wrote:I am not surprised at this, any more than the apostles were at the conduct of Nero at Rome. But the smothered heat of a volcano, will generally burst forth and give sufficient time to escape its “dreadful lava”
Joseph Smith, Journal, April 1843 wrote:In the office most of the day. Some rain and wind
A volcano broke out near Kanigshatte, in Silesia
In addition, the destructive nature caused by volcanos around the world are mentioned multiple times in the official publications of the Church. The following is of particular interest:
Times and Seasons, February 1844 wrote:VOLCANO IN GEORGIA.
The editor of the Athens (Ga.) Banner bas been informed by a gentleman in whom he places the most implicit confidence, that there is a mountain in Raibun county, in that state, which is now throwing out immense quantities of very black, dense smoke, and manifests the appearance of being volcanic. It is said that the smoke issues through fissures in the rock, and that there is a continued rumbling sound constantly heard in the bowels of the mountain, resembling that of low, distant thunder.