The job site I recently got assigned to (it's actually three sites, one location) is our current primary project with many others starting soon. I don't want to be stuck at this site too long. It costs me $1000 in gas a month, a minimum of three hours a day driving, and it's in the snow and I have a two wheel drive truck. It also rarely gets above 32° during the day so I am freezing all day. He has given me money in the past for gas, but said once my new pay schedule got implemented (which it has already) I would need to pay for my own gas. This is in California if that matters.
You "relay to your boss" by talking to your boss. Tell them your issues and ask if anything can be done about them.
If the answer is no, you get to decide whether you can tolerate this or want to quit over it. Our standard advice here is not to quit until you have a signed contract, with a start date, for the new job (but allow for a proper notice period).
Note that miles driven to somewhere other than your official work location/office are tax deductible in the US, so you may be able to recapture at least some of that cost. Can't vouch for elsewhere, and it depends on how your workplace is defined.
I'm guessing you actually want your boss to assign you to a less onerous job?
There are two sides to this: you hate the job for all the reasons you listed, your boss needs someone to do the work you've been assigned.
The best way to get out of it is to give you boss an alternative solution. Perhaps there's someone else who would be happier to do the work, someone who lives closer or doesn't mind the cold? Or perhaps you could persuade your boss to give you an allowance to stay closer to the site? Or do some of the work off-site?
At the moment your boss has one problem which is getting the work done so that your employer gets paid. When you talk to him you don't want to leave him feeling that he's got two problems: the work and your willingness to do the work. Try to find a way to get yourself out of the situation without too much of a downside for your boss.
Of course if there are no alternatives it becomes a matter of suck-it-up or quit.
The issues you mention are things managers always take into account. Chances are that your boss is already aware and they know that you don't like it.
You can openly say that you don't like it. But when you say it you should also pay close attention to the body language. If he is telling you that the kind of refund you had in the past is no longer available in fact he is also cutting your pay. Bosses do this kind of thing only when they have a replacement available. So, you should try to understand how much he is willing to retain you.