Yes, Jessica ( @ Jessica, hi! how r u?) is right. Mirai is 未来. It means "future" in Japanese.
Is this sentence a part of lyric or song? because it seems very metaphorical, especially the first sentence;" Horahora to temaneku mirai"
If I rewrite this sentence to make it gramatically correct, I would write " Mirai ga horahora to (watashi o) temaneku."(未来がほらほらと(わたしを)手招く). As you may know, temaneku(手招く) or temanekisuru (手招きする) is an action of beckon when someone calls someone to come here. and " horahora" is a call we often say when we beckon someone.
For example, "母親は”ほらほら”といいながら子供を手招きした” ””ほらほら、こっちに来なさい”と先生に手招きされて、私は黒板に向かった” etc.
In case of your sentence ,I would translate "Future beckons me saying " horahora" in English.
Without saying "I will forward to future" but saying "Mirai calls me" ( same as taking inanimate in English), this sentence seems indicate that "I can't escape my fate." because future calls me = I am drawn by future.
And the last sentence, it is right, Eliot. It means"What's going to happen from now on".
I think she seems to be a little bit afraid of her future, because she can't escape from fate, so she will just let her future leave, and wait for what's happening.
I might confuse you guys, but hopefully u can understand a little bit.
Thank you.