There are advantages in crate training. If you don't use the crate as a punishment site, your dog comes to think of it as his own little space and loves it.
When we have a new puppy at our house (we're raising our ninth pup for Canine Companions for Independence), we have to treat him/her as a new baby! He doesn't know anything and needs constant supervision. I have to take him out (NOT send him out) to potty and that's no fun in winter, but it's part of the job.
Even though it's cold where you live, you need to take him out first thing in the morning, after he eats, last thing at night, after he wakes up from a nap, and about once an hour otherwise. As he grows, you can make that one-hour time longer, but don't forget that he doesn't know what to do yet. When he makes a mistake in the house (!), pick him up, get him outside, and give him whatever command you're using to tell him to potty there. In all cases, pick him up and take him out, let him do his thing with you standing there, praise him highly, and bring him in. After that you can clean up the mess. At nighttime, you could cut off his available water about 8 p.m. - it might help him not to need to go so often during sleep time. (Consider also putting an old towel over the door of the crate, so it's darker and he has fewer outside distractions.)
During the night, when he cries, first get your boots and coat on quickly, and then get him out of the crate (carry him if you can, and/or put him on leash), take him right out to his spot, give the command and wait for him to go, and take him right back in. (Not exactly immediately - you might want to wait outside another minute in case he needs to do something else.) Praise him and put him right back in his crate.
Keep him on leash at night for pottying for several weeks, because he's going to think, "Now that I'm awake and out here, why not play?" But playtime is when the sun is out. He doesn't know that.
Eventually, you might try putting a nose-height bell or something on your door so Pup can learn to let you know when he needs to go out. He'll probably start picking up cues from your other Boxer.
You're going to get some fussing, because he's just a baby and understandably doesn't want to be alone (and also because he wants to find out which of your buttons he can push). Make sure he has safe things in the crate to chew. If you can wait out the fussing, he'll realize that the game won't work, and you'll know then that if he fusses in the crate it's for a legitimate reason. (If you can keep the crate in or very near your room, he'll feel like Mama is nearby and be a little more comfortable.)
What size is his crate? He needs to be able to stand up and turn around comfortably. If you've purchased one for the long run and it's really big, stick some cardboard boxes in the back to make it smaller. You don't want him to have room to answer the call of nature comfortably inside the crate and still sleep there.
During the day, always keep him where you can keep an eye on him. He's a baby, he's interested in everything, and he has the brains (and the attention span) of a FRUIT FLY. He will put his little puppy teeth on anyone and anything. Puppy-proof the rooms where he is allowed to be. Try to keep toys posted in good places so one is at hand when he starts in on somebody's feet. Say, "Don't," or whatever your chosen command is. Give him the toy instead.
When you try leaving the pup alone in his crate during the day, start out with a very short time. When he's tired anyhow (this works best!), put him in his crate with a chew toy, cover the door with the towel, and leave for maybe twenty or thirty minutes. Come back in, make just a little fuss but not too much, praise him, and take him right outside for you-know-what. As he gets older (and his bladder will hold more longer), you can lengthen the time. In your case, you may eventually want to teach him to stay home without being in his crate, because that's what your other dog does. But don't do that until the pup is totally trustworthy! (And that's quite a while.)
I'm always exhausted with a new puppy. But new ones get bigger, and they develop some brains, and eventually we have a dog who knows what to do and where to "go." Have fun with him!
