You can use "walk around" without an object. Sometimes you can use the Present Continuous to talk about plans or arrangements in the future, but since you used the adverb "today" the way you said it sounds like you're walking now. Add the adverb "later" after "around" to clarify your intended meaning.

Present participles, by themselves, do not create any time frame. All that the sentence "We are walking" does is to attach "walking" as an adjective to the pronoun "we". That's all it does. It does nothing more. Consider the descriptions of the "present continuous tense" you find in grammar books to be nothing more than helpful guides to the most common possibilities of what it might mean. What it actually means depends on context. The time could be past, present, or future. Yes, it can even be past. Here's an example. Consider this conversation over the phone at noon on a sunny day. In the morning, Beth took a walk with her family and they plan to see a movie in the afternoon. Jane: Hi, Beth, what's up? What are you guys doing today? Beth: Oh, we're playing games, eating, walking around, and going to a movie. That is a valid use of "walking around" even though the walking part of Beth's day is already finished. On the basis of what Beth said, Jane has no way of knowing whether the walking is in the past, present, or future. All she knows is that the adjective "walking" describes the family in some unspecified way.

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Today the weather is warm so we're walking around = present... happening right now. Today the weather is warm so we're going to walk around = future.

'We're walking around' would be used in present, generally, if you were currently walking around. Sometimes people do talk like this when they are announcing future plans, though. In your sentence, it includes 'today' marking that it will occur on that day--so, this makes it more clear. If you want to discuss the future more clearly, just insert 'going to be.' 'The weather is warm today, so we're going to be walking around.' Or: '...so we'll be walking around.' Or, more simply: '...going to walk around.' So, yeah, you can say it like that, especially if it's like an announcement of intention, but without context, it could be unclear/odd.