A thin coating of ice in the middle of winter will typically have no ill effects on trees.
In fact, long periods of ice coating fruit trees is thought it could reduce mite and insect populations by suffocating the eggs that were laid last fall. In some cases, ice will protect tender fruit buds.
So, the first answer is “No”.
As ice loads increase, especially on evergreens, branches can begin to break. Heavy snow or ice after trees begin to leaf out like we experienced last spring can cause branches to break. This can be especially dangerous if the tree has internal rot.
So, the answer is “Yes”.
So why did I say Maybe??
Because in the case of ice and snow, the variables of duration and amount of snow or ice will determine the amount of damage. This is particularly true when an ice storm will down power lines.
If you’re not sure your tree can withstand a heavy ice load, especially if it is growing near power lines, refer to the article I wrote last week:
https://bygl.osu.edu/node/1922
One thing is for sure, Ice coated trees are beautiful.