The Spiritually Dead "Tares"
The underlying Greek (Jude 1:12—W&H-NA27),for reference, is:
Οὗτοί εἰσιν ... νεφέλαι ἄνυδροι ὑπὸ ἀνέμων παραφερόμεναι δένδρα φθινοπωρινὰ ἄκαρπα δὶς ἀποθανόντα ἐκριζωθέντα
Quite literally, then,
These are ... waterless clouds, being carried about by winds, autumnal trees, fruitless, twice having died, being uprooted.
Now this isn't a translation into English, because no translation should be what is called 'slavish.' So, in English, I would translate this:
These [men] are ... clouds without water, carried about by the wind; fruitless trees of autumn, doubly dead (being uprooted).
St. Jude is making exhaustively and superfluously clear just how morally and spiritually bankrupt these tares are.1 Not about particular trees.
Not only are they trees of autumn (not late autumn, or of any particular kind), and therefore already considered 'dead' (not producing fruit, useless, often ugly, bare, paling in comparison to their proper glory), but he goes on to describe these dead trees as fruitless (ἄκαρπα—not-fruit-having) (deliberately redundant, it seems, given they are autumn trees), and not only that, but they are not just dead, but twice dead, and to top it off, they have been uprooted,2 making their existence even more futile.
Futility and fruitlessness here, of course, is a description of their spiritual fruitlessness, not being borne by the Spirit of God, but, as it were, wherever the wind takes them.
The Petrine Parallel
St. Peter also speaks of this in his second Epistle, which is somewhat parallel to Jude's Epistle (without doubt both come form the same source of doctrine in the places which correspond).
The verse in question, describing the very same people, having slipped in among the church:
2 Peter 2:17
οὗτοί εἰσιν πηγαὶ ἄνυδροι καὶ ὁμίχλαι ὑπὸ λαίλαπος ἐλαυνόμεναι οἷς ὁ ζόφος τοῦ σκότους τετήρηται
These [men] are dry springs, and mists dispersed by the storm, for whom the gloom of darkness has reserved.
What is more useless than a spring that gives no water—a dry spring (the same word ἄνυδροι translated differently). Intentionally oxymoronic, it indicates a failure to do what one is supposed to do, or here, be what one is supposed to be, namely a Christan, especially when one tends to one's needs among its members, as if he were one of them. But they are not objectively of the church, even though they might subjectively superficially appear to be: "They went out from us, but they were not of us; for if they had been of us, they would have continued with us: but they went out, that they might be made manifest that they all are not of us" (1 Jn 2:19).
A mist dispersed by the storm might refer to what Jesus taught about the growing cold, or inability to remain firm, being baseless and not ground in Christ, when faced with the trial Jesus promises will follow His believers:3
Matthew 7:24-27 (ASV)
Every one therefore that heareth these words of mine, and doeth them, shall be likened unto a wise man, who built his house upon the rock: and the rain descended, and the floods came, and the winds blew, and beat upon that house; and if fell not: for it was founded upon the rock. And every one that heareth these words of mine, and doeth them not, shall be likened unto a foolish man, who built his house upon the sand: and the rain descended, and the floods came, and the winds blew, and smote upon that house; and it fell: and great was the fall thereof.
Matthew 24:12 (ASV)
And because iniquity shall be multiplied, the love of the many shall wax cold. But he that endureth to the end, the same shall be saved.
"turning the grace of our God into lasciviousness" (1:4) refers to taking for ganted and therefore abusing the reconciliation recieved in Christ, worked by grace, utlimately, unto their own damnation (2 Pt 2:1,22; 3:16; Heb 10:29; Rom 6:12-13,16).
1 cf. Mt 3:12; 13:25,30
2 cf. Mt 3:10; 7:19; Jn 15:2
3 Mt 10:22; Jn 15:29-20; Phil 1:29; cf. Jas 1:3-4