Low thyroid hormone will effects sugar levels in that it may reduce pancreatic function so influencing the release of insulin and glucagon, slowing glucose absorption in the gut, the rate our cells uptake glucose, the response of insulin secretion and the clearance of too much in the blood.
Are you diabetic or have insulin resistance ? ? .. You can have too much sugar in the blood (insulin resistance) or too little sugar in the blood (hypoglycaemia)
A healthy snack (ie: cheese & apple, etc) shouldn't encourage large blood sugar elevations as the protein and fats will level things out (& keep you feeling full for longer.) Snacking on sugary things can encourage insulin resistance and mess up cortisol levels as every time you have a blood sugar drop, your adrenals will secrete cortisol to increase glucose, especially to the brain to stop you feeling light headed..
If continual (ie lots of sugary snacking) this extra cortisol can inhibit conversion of T4 - T3, cause thyroid hormone receptor insensitivity (meaning that even if T3 levels are high enough, they may not be able to bind normally to receptor sites) and suppress pituitary function.
Eating regular meals with protein, healthy fats and low GI carbs will encourage good blood sugar levels and thyroid function.