I found three good articles about pruning evergreens, and hemlock in particular. Please follow the links below and read the full articles. They are short and have lots of additional insight. The italicized lines below are excerpted from the articles and are particularly helpful.

Pruning Evergreens – Wisconsin Horticulture

Hemlocks, arborvitae, and yews: These evergreen trees and shrubs have latent (dormant) buds farther back down the stem. Therefore, you can shear these evergreens in late spring or early summer after new growth has expanded. You can also prune them in spring before the new growth has expanded because any subsequent growth will hide the pruning cuts. You can also prune individual branches back to a bud or a branch to encourage more compact habit. If these evergreens are used in formal hedges, maintain the base of the hedge wider than the top to insure adequate light penetration to the bottom of the hedge.

Pruning Needled Evergreens (psu.edu)

Timing is important. Species differ in the best time to prune them depending on purpose. Conifers are very resinous, so pruning when their sap is running is discouraged for some species. The best time is usually late winter to early spring before new growth develops. One exception, of course, is for safety. Prune dangerous branches anytime.

Pruning Evergreens | Cooperative Extension | University of Delaware (udel.edu)

4. The YEW and HEMLOCK Group. It is preferable to allow these plants to retain their natural form, but both respond well to heavy pruning and shearing. Yews are able to withstand exceptionally severe pruning into the older wood. Early spring is the best time for pruning but occasional light pruning later in the season may be necessary.

The most common thought in everything I found is that you should do your pruning in late winter / early spring prior to the sap beginning to run and before the new growth is fully expanded. The article from the University of Wisconsin differs somewhat, perhaps because they are further north with cooler summers. That said, if the low hanging branches are causing a problem with mowing or other work, I would not hesitate to remove them now. The risk of insect or disease may be increased somewhat but if the tree is otherwise healthy it should be okay.

Thank you for your query. I hope this has been helpful.

Dear botanygal47, here's the response to your question:

I found three good articles about pruning evergreens, and hemlock in particular. Please follow the links below and read the full articles. They are short and have lots of additional insight. The italicized lines below are excerpted from the articles and are particularly helpful.

Pruning Evergreens – Wisconsin Horticulture

Hemlocks, arborvitae, and yews: These evergreen trees and shrubs have latent (dormant) buds farther back down the stem. Therefore, you can shear these evergreens in late spring or early summer after new growth has expanded. You can also prune them in spring before the new growth has expanded because any subsequent growth will hide the pruning cuts. You can also prune individual branches back to a bud or a branch to encourage more compact habit. If these evergreens are used in formal hedges, maintain the base of the hedge wider than the top to insure adequate light penetration to the bottom of the hedge.

Pruning Needled Evergreens (psu.edu)

Timing is important. Species differ in the best time to prune them depending on purpose. Conifers are very resinous, so pruning when their sap is running is discouraged for some species. The best time is usually late winter to early spring before new growth develops. One exception, of course, is for safety. Prune dangerous branches anytime.

Pruning Evergreens | Cooperative Extension | University of Delaware (udel.edu)

4. The YEW and HEMLOCK Group. It is preferable to allow these plants to retain their natural form, but both respond well to heavy pruning and shearing. Yews are able to withstand exceptionally severe pruning into the older wood. Early spring is the best time for pruning but occasional light pruning later in the season may be necessary.

The most common thought in everything I found is that you should do your pruning in late winter / early spring prior to the sap beginning to run and before the new growth is fully expanded. The article from the University of Wisconsin differs somewhat, perhaps because they are further north with cooler summers. That said, if the low hanging branches are causing a problem with mowing or other work, I would not hesitate to remove them now. The risk of insect or disease may be increased somewhat but if the tree is otherwise healthy it should be okay.

Thank you for your query. I hope this has been helpful.

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