I can tell you what Catholicism has to say about it, for the most part. Though, if you're looking for some survey of western Christians to get some sense of what all of them think mysticism is, this isn't the forum for that. But, even without a poll, I can say with high confidence that most Christians, especially those from larger denominations like Catholicism, don't know their own doctrines sufficiently. And they likely have no idea what what we mean when we call one of our saints a mystic.
That said, proper mysticism is not emotionalism, and it's not anti-rational; it's superrational.
Christian mysticism is the "quest" to come into an intimate, unitive relationship with God, God willing. And since God is well-beyond comprehension, mystical experiences and practices are necessarily "foggy" and "mysterious." However, the fruits of a mystical experience (the fruits of contemplation) can always be verified rationally by comparing their message with that of Word of God and the Church.
But, the best way to see that proper mysticism is not an emotionalism, I think, is to examine some mystics, their experiences, and their insights. You'll definitely find some emotional experiences in their bios. And, you should expect to find emotion in a relationship. But, these aren't the highlights of their stories. The highlights are the ecstatic, confusing climaxes of their contemplative experiences, and the fruits that follow. Unlike what an emotional experience can yield, these experiences yield prophetic and/or genius-like insight, transcendent peace, and profound love (in the sense of willing the good of others as other).
Two very notable Catholic mystics.
- St. Theresa of Avila (on Wikipedia and Catholic Encyclopedia)
- St. John of the Cross, Doctor of mystic theology (on Wikipedia and Catholic Encyclopedia)
And I think it has been well-argued that John the Apostle and St. Paul were mystics. And you can refer to their NT writings. The Gospel of John, in particular, has a pretty heavy mystical feel to it.
I think it's also important to point out that Christianity -- Catholicism and Orthodoxy in the least -- are highly mystical religions. We don't necessarily call every Christian a mystic, but the practices (even basic prayer) have an end-goal that is ultimately mystical. That is, we're trying to unite with God in whatever manner God desires. And, we acknowledge that this relationship is beyond understanding (it's a mystery),but we work with God to attain (receive) that unity anyway -- that's mysticism.
But again, if you're looking for an answer that represent what most Christians believe, regardless of the dogma to which they subscribe, I'd wager most of them have little to no idea what mysticism is.