<slide across the ice><glide over the ice>

An example sentence using "slide" in Longman Contemporary: Francesca slid across the ice.

An example sentence using "glide" in Oxford Learner's Dictionaries: The skaters were gliding over the ice.

Are slide and glide interchangeable in this context?

In the context of moving over ice, yes.

Depending on context, even on ice, they might not be interchangeable. Someone could slide on their front, their back, in control, out of control, arms and legs all over the place, as a result of purposeful action or of an accident.
Gliding carries a sense of elegance and poise, and suggests that the person is probably in control and on their feet.

WilliamTaft said:

Are slide and glide interchangeable in this context?

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You shouldn't ask this. No two words are 'interchangeable'. Focus on the meaning and use of each word.

Oxford Learner's Dictionary:
interchangeable
that can be exchanged, especially without affecting the way in which something works
The two words are virtually interchangeable (= have almost the same meaning).

Thanks for the info.

WilliamTaft said:

An example sentence using "slide" in Longman Contemporary: Francesca slid across the ice.

An example sentence using "glide" in Oxford Learner's Dictionaries: The skaters were gliding over the ice.

Are slide and glide interchangeable in this context?

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You haven't really given any context. It would be more useful if you give us a sentence to consider.

WilliamTaft said:

The skaters were gliding over the ice.

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I wouldn't use "slide" there. It's hard to say why except "glide" is more suggestive of purposeful activity. Also, it has the connotation of grace. Using the word "glide" helps you imagine them doing something like ballet