Your question cannot be answered with the information that you have provided. First we need to understand what you mean by 'ice'. Water, hydrocarbons, and low temperatures and high pressures can make ice (solid water phase), hydrates (solid hydrocarbon and water), and even solid CO2 (under the right conditions but I doubt you will see these in a deethanizer).
To evaluate this possibility you will at least need some compositions (and some details around the tower would help). What is the water content? (As an example we have deethanizers that have water dew points in the feed that are -20F and some that are -100F or lower). What is the rest of the stuff? The mix of other materials will tell you what sort of hydrate formation potential you have. In a lot of cases you will form hydrates well before you form actual 'ice'.