It seems the OP didn't asked the love marriage, which is today so common and seems he know the fact that it is prohibited and asking whether Islam recognizes natural love between opposite sex.
Yes, Islam does of course recognize love between a boy and a girl (as long that do not cross the border). Because,
It is Allah himself, which created affection, desire and love between the opposite genders, as he saying
Beautified for people is the love of that which they desire - of women and sons, heaped-up sums of gold and silver, fine branded horses, and cattle and tilled land. That is the enjoyment of worldly life, but Allah has with Him the best return. source.
and saying this
Sahih International: And of His signs is that He created for you from yourselves mates that you may find tranquility in them; and He placed between you affection and mercy. Indeed in that are signs for a people who give thought. source
So, I think it is clear, Islam does not ignore this fact. (how can it ignore where Allah is the creator of such things in human nature?)
Why prophet proposed an old man?
Though you didn't mention the exact incident, I would say this:
The prophet is the messenger of Allah. Allah reveals many things to his messenger which he does not reveal to any other. May be the prophet saw, future goodness in that marriage with the old man or it may be indicated by Allah.
But, the general guideline is not this. Because, once a Sahaba got married and he informed the Prophet. The prophet asked, was she a virgin ( indicating young, same age) or a widow. The Sahaba replied, She was a widow. The prophet then said, "Why didn't you marry a women of same age? " or something similar. See here
So, marrying a man or women of same age isn't discouraged by Islam, rather it is encouraged.
Old answer (but I think, still relevant) :
First we need a real good definition on the term "Love marriage". I assume, you are asking about the general practice which involve making friendship with someone and then loving and ... etc.
On that context, I believe, that kind of Love marriage is totally unacceptable. My point of reasoning is given below:
With this saying of Allah about lowering your gaze, I don't find a way to make a friendship with someone of opposite sex. Because, making friendship usually very naturally involves at least seeing (please don't say , some hypothetical concept of making friend), then how you supposed to be loving someone, while you are not even allowed to see him/her?
If you argue that, Allah prohibits gazing but now loving, then I would say, does it make sense, if your father orders you to not to be with someone and you think it is okay to can send messages,.. etc without physically being near him/her ?
"Love marriage" in the context of current age, essentially involve being alone with the loved person, which is clearly prohibited. (Again, I am realistic and can't dream of any loving pair not being alone, especially in current age) as recorded in Tirmidhi, #2165.
"No man is ever alone with a (non-mahram) women but the Shaytaan is the third one present.”
See this similar question and this fatwa.
But, If it becomes possible to love a person without seeing him/her, not thinking anything which is not allowed and after some time goes on proposal in appropriate way and marry him/her, then I would say, it will be allowed, because it do not break any rule or order of Allah and his messenger, of course Love can exists without even seeing 1 (intentionally) someone. such as by their quality or good characters etc.
1: I am not saying it is prohibited to see someone with intention of marriage. I am saying about the general looking and gazing things
For further reading..