In ICE, you can’t get data from any arbitrary frame. You get whatever data comes though through your input ports for the current evaluation time. There’s no way (except for Get Data at Previous Frame) for you to read the scene graph at any other time than the time at which the ICE Tree operator is being evaluated.

A few related notes:

• In a simulated ICE tree, you could cache values from previous frames and then access them during playback of the simulation.
• With Get Action Source at Frame, you can get the value at a specific frame of an item stored in an animation source.
• On a non-simulated ICE tree, you might be able to use an at_frame expression (hat tip: grahamef)
• You might consider writing a custom ICE node that accesses values on other frames, but I don’t know that this such a good idea. According to the docs, that isn’t recommended for custom ICE nodes.