What I'd sort of like to say:
Hori-san,
Long time no see! It feels like it’s autumn already. I’m sorry that I haven’t been in touch recently on email, but as usual, I have been busy with work, and so haven’t had time to write in Japanese, which I still find difficult.
I just wanted to get in touch with you to thank you for arranging this trip to Hawaii. As ever, you’re very kind. I’m very much looking forward to seeing you in Hawaii.
As you know, Shino and I will be getting married next month. As you might also know, I haven’t formally proposed to her yet. I would like to ask your permission to do so. I intend to ask her to marry me in Hawaii, with my mother’s ring – which is one tradition here in England. I intend to do my best to look after her, and as you know my family are very much looking forward to welcoming her into our family. So I hope you will approve of me finally proposing to her.
Well, that’s it for now. I look forward to seeing you next week!
And here's my own stab at translating it:
堀さま
こんにちは!おひさしぶりです!もう秋になったと思っていますね。
失礼しますが最近エメエルを出しませんでした。あいかわらず仕事はとてもいそがしいですから。出したいですが日本語で書くじかんがありません。
このエメエルはありがとうと言いたいですから。ハワイイの旅行はどもうありがとうございます!あいかわらずとても親切です。堀に会いますよくたのしみです。
来月詩乃と結婚します(それでたのしいです!)。でも私はプロポサルをまだしていません。
詩乃と結婚してもいいですかと言いたいです。ハワイイで結婚のプロポサルをするつもりです。母のゆびわを使いたいです。いぎりすのしゅうかんです。詩乃と結婚させていただけませんか。
[I intend to do my best to look after her]. 私のかぞくは詩乃によく迎えたいです。[I hope you will give me your approval.]
じゃまた来週。
Any suggestions will be much appreciated!