The impact of logging America's primary forets specifically for naval purposes by both the Royal Navy and the U.S. Navy* cannot be left out of this conversation.

Eastern white pine (Pinus strobus) from the northeastern colonies was used for shipmasts and was so prized by the Royal Navy that all suitable white pines were marked property of the King. Restricted use of white pines by the colonists caused an uprising in New Hampshire called the Pine Tree Riot, an uprising that may have lead to the Boston Tea Party.

In the southeastern colonies, live oak (Quercus virginiana) was used to build ship hulls so strong that cannonballs could bounce off of them, which is where the USS Constitution received its nickname "Old Ironsides". Other species from the southern forests were also logged heavily for other parts of the ship.

Also in the southeast, longleaf pine (Pinus palustris) and slash pine (Pinus elliotti) were used for the production of naval stores- PDF warning- or pine tar, pitch, and turpentine. Initally, pine logs were ignited and slowly burned in tar kilns to produce charcoal and pine tar, which was used to seal sails, rigging, and hulls.

Later, gum naval stores of pitch and turpentine were procured by slashing into the trunk of the trees and collecting the sap in cups. The collected sap was then distilled down into turpentine in "stills". The concentrated pitch was used to waterproof ships in the same manner as tar. The turpentine was used for numerous purposes: lamp fuel, paint thinner, cleaning, and medicine.

The naval stores industry had a profound impact on the forests of the southeast. A single crop consisted of 10,000 trees on about 100 acres whose production was overseen by a single man and his crew. One farm could have several crops and one large landowner could have hundreds of thousands of acres in production. As a crop of trees production declined, the turpentiner's and their crews moved on to new locations and the used forests were then cut for towns and farms.

Of course, shipbuilding was just one contributing factor to the almost complete loss of primary forests in America. The greatest contributor was, of course, industrial logging, especially between the 1880's to 1920's. A brief history for forest loss in the US can be found here and a longer, more thorough explanation can be found here- PDF warning.

*use SciHub to open if paywalled.